Mathematische Nachrichten最新文献

{"title":"Curvature of quaternionic skew-Hermitian manifolds and bundle constructions","authors":"Ioannis Chrysikos,&nbsp;Vicente Cortés,&nbsp;Jan Gregorovič","doi":"10.1002/mana.202400301","DOIUrl":"https://doi.org/10.1002/mana.202400301","url":null,"abstract":"<p>This paper is devoted to a description of the second-order differential geometry of torsion-free almost quaternionic skew-Hermitian manifolds, that is, of quaternionic skew-Hermitian manifolds <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>,</mo>\u0000 <mi>Q</mi>\u0000 <mo>,</mo>\u0000 <mi>ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(M, Q, omega)$</annotation>\u0000 </semantics></math>. We provide a curvature characterization of such integrable geometric structures, based on the holonomy theory of symplectic connections and we study qualitative properties of the induced Ricci tensor. Then, we proceed with bundle constructions over such a manifold <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>,</mo>\u0000 <mi>Q</mi>\u0000 <mo>,</mo>\u0000 <mi>ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(M, Q, omega)$</annotation>\u0000 </semantics></math>. In particular, we prove the existence of almost hypercomplex skew-Hermitian structures on the Swann bundle over <i>M</i> and investigate their integrability.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"87-112"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400301","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120095","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":"Laplacian with singular drift in a critical borderline case","authors":"D. Kinzebulatov","doi":"10.1002/mana.202400098","DOIUrl":"https://doi.org/10.1002/mana.202400098","url":null,"abstract":"<p>We establish well-posedness and regularity results for parabolic diffusion equation on the torus in the case when the singularities of a general drift reach the critical magnitude. The latter dictates the need to work in an Orlicz space situated between all <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$L^p$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$L^infty$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"511-526"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397233","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":"Decay character and global existence for weakly coupled system of semilinear \u0000 \u0000 σ\u0000 $sigma$\u0000 -evolution damped equations with time-dependent damping","authors":"Cung The Anh,&nbsp;Phan Duc An,&nbsp;Pham Trieu Duong","doi":"10.1002/mana.202400243","DOIUrl":"https://doi.org/10.1002/mana.202400243","url":null,"abstract":"<p>In this article, we investigate the existence and decay rate of the global solution to the coupled system of semilinear structurally damped <span></span><math>\u0000 <semantics>\u0000 <mi>σ</mi>\u0000 <annotation>$sigma$</annotation>\u0000 </semantics></math>-evolution equations with time-dependent damping in the so-called effective cases\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"478-510"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397234","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":"Embedded trace operator for infinite metric trees","authors":"Valentina Franceschi,&nbsp;Kiyan Naderi,&nbsp;Konstantin Pankrashkin","doi":"10.1002/mana.202300574","DOIUrl":"https://doi.org/10.1002/mana.202300574","url":null,"abstract":"<p>We consider a class of infinite weighted metric trees obtained as perturbations of self-similar regular trees. Possible definitions of the boundary traces of functions in the Sobolev space on such a structure are discussed by using identifications of the tree boundary with a surface. Our approach unifies some constructions proposed by Maury, Salort, and Vannier for discrete weighted dyadic trees (expansion in orthogonal bases of harmonic functions on the graph and using Haar-type bases on the domain representing the boundary), and by Nicaise and Semin and Joly, Kachanovska, and Semin for fractal metric trees (approximation by finite sections and identification of the boundary with a interval): We show that both machineries give the same trace map, and for a range of parameters we establish the precise Sobolev regularity of the traces. In addition, we introduce new geometric ingredients by proposing an identification with arbitrary Riemannian manifolds. It is shown that any compact manifold admits a suitable multiscale decomposition and, therefore, can be identified with a metric tree boundary in the context of trace theorems.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"190-243"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300574","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120065","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":"The first eigenvalue of one-dimensional elliptic operators with killing","authors":"Kang Dai,&nbsp;Xiaobin Sun,&nbsp;Jian Wang,&nbsp;Yingchao Xie","doi":"10.1002/mana.202400331","DOIUrl":"https://doi.org/10.1002/mana.202400331","url":null,"abstract":"<p>In this paper, we investigate the first eigenvalue for one-dimensional elliptic operators with killing. Two-sided approximation procedures and basic estimates of the first eigenvalue are given in both the half line and the whole line. The proofs are based on the <span></span><math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math>-transform, Chen's dual variational formulas, and the split technique. In particular, a few examples are presented to illustrate the power of our results.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"282-311"},"PeriodicalIF":0.8,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143120097","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":"Averaging principle on semi-axis for semi-linear differential equations","authors":"David Cheban","doi":"10.1002/mana.202300392","DOIUrl":"https://doi.org/10.1002/mana.202300392","url":null,"abstract":"<p>We establish an averaging principle on the real semi-axis for semi-linear equation\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"156-189"},"PeriodicalIF":0.8,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118142","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":"Well-posedness and inviscid limits for the Keller–Segel–Navier–Stokes system of the parabolic–elliptic type","authors":"Taiki Takeuchi","doi":"10.1002/mana.202300304","DOIUrl":"https://doi.org/10.1002/mana.202300304","url":null,"abstract":"<p>We show the local well-posedness of the Keller–Segel system of the parabolic–elliptic type coupled with the Navier–Stokes system for arbitrary initial data with Sobolev regularities, where the solution is uniformly bounded with respect to the viscosity. We also show the continuous dependence of the solutions with respect to the initial data. As a result of the uniform boundedness of the solutions, we obtain inviscid limits of the system. The proof is mainly based on a priori estimates in the Sobolev spaces.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"53-86"},"PeriodicalIF":0.8,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117468","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":"Fractional Laplacian in V-shaped waveguide","authors":"Fedor Bakharev,&nbsp;Sergey Matveenko","doi":"10.1002/mana.202400271","DOIUrl":"https://doi.org/10.1002/mana.202400271","url":null,"abstract":"<p>The spectral properties of the restricted fractional Dirichlet Laplacian in <span>V</span>-shaped waveguides are studied. The continuous spectrum for such domains with cylindrical outlets is known to occupy the ray <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <msub>\u0000 <mi>Λ</mi>\u0000 <mo>†</mo>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mo>+</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$[Lambda _dagger, +infty)$</annotation>\u0000 </semantics></math> with the threshold corresponding to the smallest eigenvalue of the cross-sectional problems. In this work, the presence of a discrete spectrum at any junction angle is established along with the monotonic dependence of the discrete spectrum on the angle.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"427-436"},"PeriodicalIF":0.8,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397039","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":"Seshadri constants on blow-ups of Hirzebruch surfaces","authors":"Krishna Hanumanthu,&nbsp;Cyril J. Jacob,&nbsp;B. N. Suhas,&nbsp;Amit Kumar Singh","doi":"10.1002/mana.202400018","DOIUrl":"https://doi.org/10.1002/mana.202400018","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;mi&gt;e&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;≥&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$e,r ge 0$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be integers and let &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;F&lt;/mi&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mi&gt;⊕&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;O&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathbb {F}_e: = mathbb {P}(mathcal {O}_{mathbb {P}^1} oplus mathcal {O}_{mathbb {P}^1}(-e))$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; denote the Hirzebruch surface with invariant &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;annotation&gt;$e$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. We compute the Seshadri constants of an ample line bundle at an arbitrary point of the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;annotation&gt;$r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-point blow-up of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$mathbb {F}_e$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$r le e-1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and at a very general point when &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$r=e$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; or &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"437-455"},"PeriodicalIF":0.8,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143397040","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":"Infinitely many low- and high-energy solutions for double-phase problems with variable exponent","authors":"Chun-Bo Lian,&nbsp;Qing-Hai Cao,&nbsp;Bin Ge","doi":"10.1002/mana.202300284","DOIUrl":"https://doi.org/10.1002/mana.202300284","url":null,"abstract":"<p>The aim of this paper is the study of double-phase problems with variable exponent. Using the Clark's theorem and the symmetric mountain pass lemma, we prove the existence of infinitely many small solutions and infinitely many large solutions, respectively.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 1","pages":"142-155"},"PeriodicalIF":0.8,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143114308","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}