Mathematische Nachrichten最新文献

{"title":"Convergence results and optimal control problems via gap functions for n-player generalized multiobjective games with applications","authors":"Nguyen Van Hung,&nbsp;Andre A. Keller","doi":"10.1002/mana.12026","DOIUrl":"https://doi.org/10.1002/mana.12026","url":null,"abstract":"<p>The aim of this paper is to study some new results on the convergence of solutions for controlled systems driven by generalized multiobjective games, optimal control problems where the systems are governed by generalized multiobjective games and controlled systems of traffic networks. First, we recall the controlled systems of generalized multiobjective games proposed by Hung and Keller (Math. Nachr. <b>296</b> (2023), 3676–3698). Second, we introduce gap functions and a key Assumption 3.6 using nonlinear scalarization functions for these games. Results on the lower convergence and convergence of the solutions for such problems using the key Assumption 3.6 are established. Third, we revisit optimal control problems governed by generalized multiobjective games. We investigate necessary and sufficient conditions for the convergence of solutions to optimal control problems. Finally, as a real-world application, we consider the special case of controlled systems of traffic networks. The necessary and sufficient conditions for the convergence of solutions for these problems are also obtained. Many examples are given for the illustration of our results.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 6","pages":"1989-2013"},"PeriodicalIF":0.8,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144281418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The 2-divisibility of divisors on K3 surfaces in characteristic 2","authors":"Toshiyuki Katsura,&nbsp;Shigeyuki Kondō,&nbsp;Matthias Schütt","doi":"10.1002/mana.12024","DOIUrl":"https://doi.org/10.1002/mana.12024","url":null,"abstract":"<p>We show that K3 surfaces in characteristic 2 can admit sets of <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math> disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <mn>8</mn>\u0000 <mo>,</mo>\u0000 <mn>12</mn>\u0000 <mo>,</mo>\u0000 <mn>16</mn>\u0000 <mo>,</mo>\u0000 <mn>20</mn>\u0000 </mrow>\u0000 <annotation>$n=8,12,16,20$</annotation>\u0000 </semantics></math>. More precisely, all values occur on supersingular K3 surfaces, with exceptions only at Artin invariants 1 and 10, while on K3 surfaces of finite height, only <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <mn>8</mn>\u0000 </mrow>\u0000 <annotation>$n=8$</annotation>\u0000 </semantics></math> is possible.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 6","pages":"1964-1988"},"PeriodicalIF":0.8,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.12024","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144281417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On birational automorphisms of double EPW-cubes","authors":"Simone Billi,&nbsp;Stevell Muller,&nbsp;Tomasz Wawak","doi":"10.1002/mana.12022","DOIUrl":"https://doi.org/10.1002/mana.12022","url":null,"abstract":"<p>We give a classification of finite groups of symplectic birational automorphisms on manifolds of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <msup>\u0000 <mn>3</mn>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mn>3</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$textnormal {K3}^{[3]}$</annotation>\u0000 </semantics></math>-type with stable cohomological action. We describe the group of polarized automorphisms of a smooth double EPW-cube. Using this description, we exhibit examples of projective hyperkähler manifolds of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <msup>\u0000 <mn>3</mn>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mn>3</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$textnormal {K3}^{[3]}$</annotation>\u0000 </semantics></math>–type of maximal Picard rank with a symplectic action of a large group.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 6","pages":"1943-1963"},"PeriodicalIF":0.8,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144281591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Calderón reproducing formulae on product spaces of homogeneous type and their applications","authors":"Ziyi He,&nbsp;Xianjie Yan,&nbsp;Dachun Yang","doi":"10.1002/mana.12014","DOIUrl":"https://doi.org/10.1002/mana.12014","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(X_1,d_1,mu _1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(X_2,d_2,mu _2)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be two spaces of homogeneous type in the sense of R. R. Coifman and G. Weiss. In this article, the authors first introduce spaces of product test functions and product approximations of the identity with exponential decay on the product space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$X_1times X_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Using these, the authors establish product continuous/discrete Calderón reproducing formulae. As applications, the Littlewood–Paley characterizations, respectively, in terms of the Lusin area function, the Littlewood–Paley &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;annotation&gt;$g$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-function, and the Littlewood–Paley &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mo&gt;∗&lt;/mo&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;annotation&gt;$g^*_{lambda }$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-function, of the Lebesgue space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 6","pages":"1839-1921"},"PeriodicalIF":0.8,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144281437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On totally umbilical and minimal surfaces of the Lorentzian Heisenberg groups","authors":"Giovanni Calvaruso,&nbsp;Marco Castrillón-Lopez,&nbsp;Lorenzo Pellegrino","doi":"10.1002/mana.12020","DOIUrl":"https://doi.org/10.1002/mana.12020","url":null,"abstract":"<p>This paper has manifold purposes. We first introduce a description of the Gauss map for submanifolds (both spacelike and timelike) of a Lorentzian ambient space and relate the conformality of the Gauss map of a surface to total umbilicity and minimality. We then focus on surfaces of the three-dimensional Heisenberg group, equipped with any of its left-invariant Lorentzian metrics. We prove that with the obvious exception of the flat case, no totally umbilical surfaces occur. On the other hand, we determine and explicitly describe several examples of minimal and constant mean curvature (CMC) surfaces.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 6","pages":"1922-1942"},"PeriodicalIF":0.8,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.12020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144281473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Groups with triangle-free graphs on \u0000 \u0000 p\u0000 $p$\u0000 -regular classes","authors":"M. J. Felipe,&nbsp;M. K. Jean-Philippe,&nbsp;V. Sotomayor","doi":"10.1002/mana.202400554","DOIUrl":"https://doi.org/10.1002/mana.202400554","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> be a prime. In this paper, we classify the <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-structure of those finite <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-separable groups such that, given any three non-central conjugacy classes of <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-regular elements, two of them necessarily have coprime lengths.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 6","pages":"1796-1807"},"PeriodicalIF":0.8,"publicationDate":"2025-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400554","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144281372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Semiclassical solutions for critical Schrödinger–Poisson systems involving multiple competing potentials","authors":"Lingzheng Kong,&nbsp;Haibo Chen","doi":"10.1002/mana.12012","DOIUrl":"https://doi.org/10.1002/mana.12012","url":null,"abstract":"<p>In this paper, a class of Schrödinger–Poisson system involving multiple competing potentials and critical Sobolev exponent is considered. Such a problem cannot be studied using the same argument for the nonlinear term with only a positive potential, because the weight potentials set <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>{</mo>\u0000 <msub>\u0000 <mi>Q</mi>\u0000 <mi>i</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>|</mo>\u0000 <mn>1</mn>\u0000 <mo>≤</mo>\u0000 <mi>i</mi>\u0000 <mo>≤</mo>\u0000 <mi>m</mi>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$lbrace Q_i(x)|1le i le mrbrace$</annotation>\u0000 </semantics></math> contains nonpositive, sign changing, and nonnegative elements. By introducing the ground energy function and subtle analysis, we first prove the existence of ground state solution <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>v</mi>\u0000 <mi>ε</mi>\u0000 </msub>\u0000 <annotation>$v_varepsilon$</annotation>\u0000 </semantics></math> in the semiclassical limit via the Nehari manifold and concentration–compactness principle. Then we show that <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>v</mi>\u0000 <mi>ε</mi>\u0000 </msub>\u0000 <annotation>$v_varepsilon$</annotation>\u0000 </semantics></math> converges to the ground state solution of the associated limiting problem and concentrates at a concrete set characterized by the potentials. At the same time, some properties for the ground state solution are also studied. Moreover, a sufficient condition for the nonexistence of the ground state solution is obtained.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 6","pages":"1808-1838"},"PeriodicalIF":0.8,"publicationDate":"2025-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144281373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Jacobian elliptic fibrations on K3s with a non-symplectic automorphism of order 3","authors":"Felipe Zingali Meira","doi":"10.1002/mana.12018","DOIUrl":"https://doi.org/10.1002/mana.12018","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a K3 surface admitting a non-symplectic automorphism &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;annotation&gt;$sigma$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of order 3. Building on work by Garbagnati and Salgado, we classify the Jacobian elliptic fibrations on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with respect to the action of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;annotation&gt;$sigma$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on their fibers. If the fiber class of a Jacobian elliptic fibration on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;NS&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{NS}(X)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is fixed by &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;annotation&gt;$sigma$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we determine the possible configurations of its singular fibers and present the equation for its generic fiber. When the Picard number of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;annotation&gt;$X$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is at least 12 and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;annotation&gt;$sigma$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; acts trivially on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;NS&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{NS}(X)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we apply the Kneser–Nishiyama method to find its Jacobian elliptic fibrations up to &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$mathcal {J}_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-equivalence. We use our method to classify them with respect to any non-symplectic automorphism of order 3 in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;Aut&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$operatorname{Aut}(X)$&lt;/annotation&gt;\u0000 &lt;/seman","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1758-1788"},"PeriodicalIF":0.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.12018","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Regularity and separation for Grušin-type p-Laplace operators","authors":"Daniel Hauer,&nbsp;Adam Sikora","doi":"10.1002/mana.12011","DOIUrl":"https://doi.org/10.1002/mana.12011","url":null,"abstract":"<p>We analyze <i>p</i>-Laplace type operators with degenerate elliptic coefficients. This investigation includes Grušin-type <i>p</i>-Laplace operators. We describe a <i>separation phenomenon</i> in elliptic and parabolic <i>p</i>-Laplace type equations, which provide an illuminating illustration of simple jump discontinuities of the corresponding weak solutions. Interestingly validity of an isoperimetric inequality for the considered setting does not imply the continuity of weak solutions to elliptic equations. On the other hand, we can establish global <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$L^1$</annotation>\u0000 </semantics></math>-<span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$L^infty$</annotation>\u0000 </semantics></math>-regularization and decay estimates of every mild solution of the parabolic Grušin-type <i>p</i>-Laplace equation.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1727-1757"},"PeriodicalIF":0.8,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.12011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local existence and nonexistence of fractional Rayleigh–Stokes equations with a superlinear source term","authors":"Yubin Liu,&nbsp;Li Peng","doi":"10.1002/mana.12010","DOIUrl":"https://doi.org/10.1002/mana.12010","url":null,"abstract":"<p>Fractional Rayleigh–Stokes equations can be described as the viscoelasticity of non-Newtonian fluids behavior for a generalized second grade fluid. In this paper, we present the monotone iteration method to investigate the nonlinear fractional Rayleigh–Stokes equations from the perspective of the supersolution. More precisely, we analyze the local existence, boundedness, and convergence of nonnegative mild solutions under the superlinear growth conditions. Further, the local nonexistence results of mild solutions are also given.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1700-1712"},"PeriodicalIF":0.8,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}