Mathematische Nachrichten最新文献

{"title":"On the stability of constant higher order mean curvature hypersurfaces in a Riemannian manifold","authors":"Maria Fernanda Elbert, Barbara Nelli","doi":"10.1002/mana.202400159","DOIUrl":"https://doi.org/10.1002/mana.202400159","url":null,"abstract":"We propose a notion of stability for constant ‐mean curvature hypersurfaces in a general Riemannian manifold and we give some applications. When the ambient manifold is a Space Form, our notion coincides with the known one, given by means of the variational problem.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176975","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":"Entropy solutions to the fully nonlocal diffusion equations","authors":"Ying Li, Chao Zhang","doi":"10.1002/mana.202400130","DOIUrl":"https://doi.org/10.1002/mana.202400130","url":null,"abstract":"We consider the fully nonlocal diffusion equations with nonnegative ‐data. Based on the approximation and energy methods, we prove the existence and uniqueness of nonnegative entropy solutions for such problems. In particular, our results are valid for the time‐space fractional Laplacian equations.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176977","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":"Localized operators on weighted Herz spaces","authors":"Kwok‐Pun Ho","doi":"10.1002/mana.202400086","DOIUrl":"https://doi.org/10.1002/mana.202400086","url":null,"abstract":"We introduce the notion of localized operators. We extend the boundedness of the localized operators from the weighted Lebesgue spaces to the weighted Herz spaces. The localized operators include the Hardy operator, the Riemann–Liouville fractional integrals, the general Hardy‐type operators, the geometric mean operator, and the one‐sided maximal function. Therefore, this paper extends the mapping properties of the the Hardy operator, the Riemann–Liouville fractional integrals, the general Hardy‐type operators, the geometric mean operator, and the one‐sided maximal function to the weighted Herz spaces.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176863","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":"A criterion for the holomorphy of the curvature of smooth planar webs and applications to dual webs of homogeneous foliations on PC2$mathbb {P}^{2}_{mathbb {C}}$","authors":"Samir Bedrouni, David Marín","doi":"10.1002/mana.202400150","DOIUrl":"https://doi.org/10.1002/mana.202400150","url":null,"abstract":"Let be an integer. For a holomorphic ‐web on a complex surface , smooth along an irreducible component of its discriminant , we establish an effective criterion for the holomorphy of the curvature of along , generalizing results on decomposable webs due to Marín, Pereira, and Pirio. As an application, we deduce a complete characterization for the holomorphy of the curvature of the Legendre transform (dual web) of a homogeneous foliation of degree on , generalizing some of our previous results. This then allows us to study the flatness of the ‐web in the particular case where the foliation is Galois. When the Galois group of is cyclic, we show that is flat if and only if is given, up to linear conjugation, by one of the two 1‐forms , . When the Galois group of is noncyclic, we obtain that is always flat.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176974","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":"Multiplicity results for critical \u0000 \u0000 p\u0000 $p$\u0000 -biharmonic problems","authors":"Said El Manouni,&nbsp;Kanishka Perera","doi":"10.1002/mana.202300535","DOIUrl":"10.1002/mana.202300535","url":null,"abstract":"<p>We prove new multiplicity results for some critical growth <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-biharmonic problems in bounded domains. More specifically, we show that each of the problems considered here has arbitrarily many solutions for all sufficiently large values of a certain parameter <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$lambda &amp;gt; 0$</annotation>\u0000 </semantics></math>. In particular, the number of solutions goes to infinity as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$lambda rightarrow infty$</annotation>\u0000 </semantics></math>. We also give an explicit lower bound on <span></span><math>\u0000 <semantics>\u0000 <mi>λ</mi>\u0000 <annotation>$lambda$</annotation>\u0000 </semantics></math> in order to have a given number of solutions. This lower bound will be in terms of an unbounded sequence of eigenvalues of a related eigenvalue problem. Our multiplicity results are new even in the semilinear case <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$p = 2$</annotation>\u0000 </semantics></math>. The proofs are based on an abstract critical point theorem.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176979","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":"Measure theoretic aspects of the finite Hilbert transform","authors":"Guillermo P. Curbera,&nbsp;Susumu Okada,&nbsp;Werner J. Ricker","doi":"10.1002/mana.202200537","DOIUrl":"10.1002/mana.202200537","url":null,"abstract":"&lt;p&gt;The finite Hilbert transform &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;annotation&gt;$T$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, when acting in the classical Zygmund space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;l&lt;/mi&gt;\u0000 &lt;mi&gt;o&lt;/mi&gt;\u0000 &lt;mi&gt;g&lt;/mi&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Ltextnormal {log} L$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; (over &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;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(-1,1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;), was intensively studied in [8]. In this note, an integral representation of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;annotation&gt;$T$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is established via the &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;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$L^1(-1,1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-valued measure &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;m&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mo&gt;↦&lt;/mo&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$m_{L^1}: Amapsto T(chi _A)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for each Borel set &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mo&gt;⊆&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Asubseteq (-1,1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. This integral representation, together with various non-trivial properties of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semant","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176980","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":"Pseudo-Ricci–Yamabe solitons on real hypersurfaces in the complex quadric","authors":"Young Jin Suh","doi":"10.1002/mana.202400087","DOIUrl":"10.1002/mana.202400087","url":null,"abstract":"<p>First, we introduce a new notion of pseudo-anti commuting for real hypersurfaces in the complex quadric <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>Q</mi>\u0000 <mi>m</mi>\u0000 </msup>\u0000 <mo>=</mo>\u0000 <mi>S</mi>\u0000 <msub>\u0000 <mi>O</mi>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msub>\u0000 <mo>/</mo>\u0000 <mi>S</mi>\u0000 <msub>\u0000 <mi>O</mi>\u0000 <mi>m</mi>\u0000 </msub>\u0000 <mi>S</mi>\u0000 <msub>\u0000 <mi>O</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$Q^m = SO_{m+2}/SO_mSO_2$</annotation>\u0000 </semantics></math> and give a complete classification of Hopf pseudo-Ricci–Yamabe soliton real hypersurfaces in the complex quadric <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>Q</mi>\u0000 <mi>m</mi>\u0000 </msup>\u0000 <annotation>$Q^m$</annotation>\u0000 </semantics></math>. Next as an application we obtain a classification of gradient pseudo-Ricci–Yamabe solitons on Hopf real hypersurfaces in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>Q</mi>\u0000 <mi>m</mi>\u0000 </msup>\u0000 <annotation>$Q^m$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176982","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":"Approximation of a two-dimensional Gross–Pitaevskii equation with a periodic potential in the tight-binding limit","authors":"Steffen Gilg,&nbsp;Guido Schneider","doi":"10.1002/mana.202300322","DOIUrl":"10.1002/mana.202300322","url":null,"abstract":"<p>The Gross–Pitaevskii (GP) equation is a model for the description of the dynamics of Bose–Einstein condensates. Here, we consider the GP equation in a two-dimensional setting with an external periodic potential in the <span></span><math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math>-direction and a harmonic oscillator potential in the <span></span><math>\u0000 <semantics>\u0000 <mi>y</mi>\u0000 <annotation>$y$</annotation>\u0000 </semantics></math>-direction in the so-called tight-binding limit. We prove error estimates which show that in this limit the original system can be approximated by a discrete nonlinear Schrödinger equation. The paper is a first attempt to generalize the results from [19] obtained in the one-dimensional setting to higher space dimensions and more general interaction potentials. Such a generalization is a non-trivial task due to the oscillations in the external periodic potential which become singular in the tight-binding limit and cause some irregularity of the solutions which are harder to handle in higher space dimensions. To overcome these difficulties, we work in anisotropic Sobolev spaces. Moreover, additional non-resonance conditions have to be satisfied in the two-dimensional case.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300322","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176877","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":"Hyers–Ulam stability of unbounded closable operators in Hilbert spaces","authors":"Arup Majumdar,&nbsp;P. Sam Johnson,&nbsp;Ram N. Mohapatra","doi":"10.1002/mana.202300484","DOIUrl":"10.1002/mana.202300484","url":null,"abstract":"<p>In this paper, we discuss the Hyers–Ulam stability of closable (unbounded) operators with some examples. We also present results pertaining to the Hyers–Ulam stability of the sum and product of closable operators to have the Hyers–Ulam stability and the necessary and sufficient conditions of the Schur complement and the quadratic complement of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mo>×</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$2 times 2$</annotation>\u0000 </semantics></math> block matrix <span></span><math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$mathcal {A}$</annotation>\u0000 </semantics></math> in order to have the Hyers–Ulam stability.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142176981","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":"Planar Choquard equations with critical exponential reaction and Neumann boundary condition","authors":"Sushmita Rawat,&nbsp;Vicenţiu D. Rădulescu,&nbsp;K. Sreenadh","doi":"10.1002/mana.202400095","DOIUrl":"10.1002/mana.202400095","url":null,"abstract":"<p>We study the existence of positive weak solutions for the following problem:\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400095","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141922265","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}