Mathematische Nachrichten最新文献_第9页

On the stability of constant higher order mean curvature hypersurfaces in a Riemannian manifold 论黎曼流形中恒定高阶平均曲率超曲面的稳定性

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-09-01 DOI: 10.1002/mana.202400159

Maria Fernanda Elbert, Barbara Nelli

引用次数: 0

Entropy solutions to the fully nonlocal diffusion equations 完全非局部扩散方程的熵解

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-09-01 DOI: 10.1002/mana.202400130

Ying Li, Chao Zhang

引用次数: 0

A criterion for the holomorphy of the curvature of smooth planar webs and applications to dual webs of homogeneous foliations on P C 2 $mathbb {P}^{2}_{mathbb {C}}$ 光滑平面网的曲率整体性判据及其在 PC2$mathbb {P}^{2}_{mathbb {C}}$ 上同质叶状体对偶网的应用

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-09-01 DOI: 10.1002/mana.202400150

Samir Bedrouni, David Marín

{"title":"A criterion for the holomorphy of the curvature of smooth planar webs and applications to dual webs of homogeneous foliations on \u0000 \u0000 \u0000 P\u0000 C\u0000 2\u0000 \u0000 $mathbb {P}^{2}_{mathbb {C}}$","authors":"Samir Bedrouni, David Marín","doi":"10.1002/mana.202400150","DOIUrl":"10.1002/mana.202400150","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>≥</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$dge 3$</annotation>\u0000 </semantics></math> be an integer. For a holomorphic <math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math>-web <math>\u0000 <semantics>\u0000 <mi>W</mi>\u0000 <annotation>$mathcal {W}$</annotation>\u0000 </semantics></math> on a complex surface <math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>, smooth along an irreducible component <math>\u0000 <semantics>\u0000 <mi>D</mi>\u0000 <annotation>$D$</annotation>\u0000 </semantics></math> of its discriminant <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Δ</mi>\u0000 <mo>(</mo>\u0000 <mi>W</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Delta (mathcal {W})$</annotation>\u0000 </semantics></math>, we establish an effective criterion for the holomorphy of the curvature of <math>\u0000 <semantics>\u0000 <mi>W</mi>\u0000 <annotation>$mathcal {W}$</annotation>\u0000 </semantics></math> along <math>\u0000 <semantics>\u0000 <mi>D</mi>\u0000 <annotation>$D$</annotation>\u0000 </semantics></math>, 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) <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Leg</mi>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation>$mathrm{Leg}mathcal {H}$</annotation>\u0000 </semantics></math> of a homogeneous foliation <math>\u0000 <semantics>\u0000 <mi>H</mi>\u0000 <annotation>$mathcal {H}$</annotation>\u0000 </semantics></math> of degree <math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math> on <math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>P</mi>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msubsup>\u0000 <annotation>$mathbb {P}^{2}_{mathbb {C}}$</annotation>\u0000 </semantics></math>, generalizing some of our previous results. This then allows us to study the flatness of the <math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math>-web <math>\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 11","pages":"3964-3981"},"PeriodicalIF":0.8,"publicationDate":"2024-09-01","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}

引用次数: 0

Multiplicity results for critical p $p$ -biharmonic problems 临界 p$p$ 双谐波问题的多重性结果

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-08-29 DOI: 10.1002/mana.202300535

Said El Manouni, Kanishka Perera

{"title":"Multiplicity results for critical \u0000 \u0000 p\u0000 $p$\u0000 -biharmonic problems","authors":"Said El Manouni, Kanishka Perera","doi":"10.1002/mana.202300535","DOIUrl":"10.1002/mana.202300535","url":null,"abstract":"We prove new multiplicity results for some critical growth <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 <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>></mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$lambda &gt; 0$</annotation>\u0000 </semantics></math>. In particular, the number of solutions goes to infinity as <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 <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 <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.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 10","pages":"3943-3953"},"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}

引用次数: 0

Measure theoretic aspects of the finite Hilbert transform 有限希尔伯特变换的度量论问题

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-08-26 DOI: 10.1002/mana.202200537

Guillermo P. Curbera, Susumu Okada, Werner J. Ricker

{"title":"Measure theoretic aspects of the finite Hilbert transform","authors":"Guillermo P. Curbera, Susumu Okada, Werner J. Ricker","doi":"10.1002/mana.202200537","DOIUrl":"10.1002/mana.202200537","url":null,"abstract":"The finite Hilbert transform <math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math>, when acting in the classical Zygmund space <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <mi>l</mi>\u0000 <mi>o</mi>\u0000 <mi>g</mi>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <annotation>$Ltextnormal {log} L$</annotation>\u0000 </semantics></math> (over <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(-1,1)$</annotation>\u0000 </semantics></math>), was intensively studied in [8]. In this note, an integral representation of <math>\u0000 <semantics>\u0000 <mi>T</mi>\u0000 <annotation>$T$</annotation>\u0000 </semantics></math> is established via the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L^1(-1,1)$</annotation>\u0000 </semantics></math>-valued measure <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>m</mi>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 </msub>\u0000 <mo>:</mo>\u0000 <mi>A</mi>\u0000 <mo>↦</mo>\u0000 <mi>T</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>χ</mi>\u0000 <mi>A</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$m_{L^1}: Amapsto T(chi _A)$</annotation>\u0000 </semantics></math> for each Borel set <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mo>⊆</mo>\u0000 <mo>(</mo>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Asubseteq (-1,1)$</annotation>\u0000 </semantics></math>. This integral representation, together with various non-trivial properties of <math>\u0000 <semant","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 10","pages":"3927-3942"},"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}

引用次数: 0

Approximation of a two-dimensional Gross–Pitaevskii equation with a periodic potential in the tight-binding limit 二维格罗斯-皮塔耶夫斯基方程在紧束缚极限下与周期势的近似关系

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-08-12 DOI: 10.1002/mana.202300322

Steffen Gilg, Guido Schneider

{"title":"Approximation of a two-dimensional Gross–Pitaevskii equation with a periodic potential in the tight-binding limit","authors":"Steffen Gilg, Guido Schneider","doi":"10.1002/mana.202300322","DOIUrl":"10.1002/mana.202300322","url":null,"abstract":"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 <math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math>-direction and a harmonic oscillator potential in the <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.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 10","pages":"3870-3886"},"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}

引用次数: 0

Pseudo-Ricci–Yamabe solitons on real hypersurfaces in the complex quadric 复二次曲面中实超曲面上的伪里奇-山边孤子

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-08-12 DOI: 10.1002/mana.202400087

Young Jin Suh

{"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":"First, we introduce a new notion of pseudo-anti commuting for real hypersurfaces in the complex quadric <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 <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 <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>Q</mi>\u0000 <mi>m</mi>\u0000 </msup>\u0000 <annotation>$Q^m$</annotation>\u0000 </semantics></math>.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 10","pages":"3904-3926"},"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}

引用次数: 0

Hyers–Ulam stability of unbounded closable operators in Hilbert spaces 希尔伯特空间中无界可闭算子的海尔-乌兰稳定性

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-08-12 DOI: 10.1002/mana.202300484

Arup Majumdar, P. Sam Johnson, Ram N. Mohapatra

引用次数: 0

Planar Choquard equations with critical exponential reaction and Neumann boundary condition 具有临界指数反应和 Neumann 边界条件的平面 Choquard 方程

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-08-09 DOI: 10.1002/mana.202400095

Sushmita Rawat, Vicenţiu D. Rădulescu, K. Sreenadh

引用次数: 0

The energy decay rate of a transmission system governed by the degenerate wave equation with drift and under heat conduction with the memory effect 由带漂移的退化波方程控制的、热传导条件下带记忆效应的传输系统的能量衰减率