Annali di Matematica Pura ed Applicata最新文献_第10页

A counterexample to (L^{infty })-gradient type estimates for Ornstein–Uhlenbeck operators Ornstein-Uhlenbeck 算子的（L^{infty }）梯度类型估计的反例

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2023-10-27 DOI: 10.1007/s10231-023-01389-w

Emanuele Dolera, Enrico Priola

{"title":"A counterexample to (L^{infty })-gradient type estimates for Ornstein–Uhlenbeck operators","authors":"Emanuele Dolera, Enrico Priola","doi":"10.1007/s10231-023-01389-w","DOIUrl":"10.1007/s10231-023-01389-w","url":null,"abstract":"<div><p>Let <span>((lambda _k))</span> be a strictly increasing sequence of positive numbers such that <span>({sum _{k=1}^{infty } frac{1}{lambda _k} < infty })</span>. Let <i>f</i> be a bounded smooth function and denote by <span>(u= u^f)</span> the bounded classical solution to </p><div><div><span>$$begin{aligned} u(x) - frac{1}{2}sum _{k=1}^m D^2_{kk} u(x) + sum _{k =1}^m lambda _k x_k D_k u(x) = f(x),quad x in {{mathbb {R}}}^m . end{aligned}$$</span></div></div><p>It is known that the following dimension-free estimate holds: </p><div><div><span>$$begin{aligned} displaystyle int _{{{mathbb {R}}}^m}! left[ sum _{k=1}^m lambda _k , (D_k u (y))^2 right] ^{p/2} !! !!!! mu _m (textrm{d}y) le (c_p)^p !! int _{{{mathbb {R}}}^m} !! |f( y)|^p mu _m (textrm{d}y),;;; 1< p < infty end{aligned}$$</span></div></div><p>where <span>(mu _m)</span> is the “diagonal” Gaussian measure determined by <span>(lambda _1, ldots , lambda _m)</span> and <span>(c_p > 0)</span> is independent of <i>f</i> and <i>m</i>. This is a consequence of generalized Meyer’s inequalities [4]. We show that, if <span>(lambda _k sim k^2)</span>, then such estimate does not hold when <span>(p= infty )</span>. Indeed we prove </p><div><div><span>$$begin{aligned} sup _{begin{array}{c} f in C^{ 2}_b({{mathbb {R}}}^m),;;; Vert fVert _{infty } le 1 end{array}} left{ sum _{k=1}^m lambda _k , (D_k u^f (0))^2 right} rightarrow infty ;; text{ as } ; m rightarrow infty . end{aligned}$$</span></div></div><p>This is in contrast to the case of <span>(lambda _k = lambda >0)</span>, <span>(k ge 1)</span>, where a dimension-free bound holds for <span>(p =infty )</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 2","pages":"975 - 988"},"PeriodicalIF":1.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01389-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136235394","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

Complex Dirac structures with constant real index on flag manifolds 旗流形上具有恒定实指数的复狄拉克结构

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2023-10-27 DOI: 10.1007/s10231-023-01394-z

Cristian Ortiz, Carlos Varea

引用次数: 0

Non-degeneracy of the multi-bump solutions to the Brezis-Nirenberg problem 布雷齐斯-尼伦堡问题多凸点解的非退化性

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2023-10-27 DOI: 10.1007/s10231-023-01395-y

Haixia Chen, Chunhua Wang, Huafei Xie, Yang Zhou

{"title":"Non-degeneracy of the multi-bump solutions to the Brezis-Nirenberg problem","authors":"Haixia Chen, Chunhua Wang, Huafei Xie, Yang Zhou","doi":"10.1007/s10231-023-01395-y","DOIUrl":"10.1007/s10231-023-01395-y","url":null,"abstract":"<div><p>We revisit the well-known Brezis-Nirenberg problem </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} -Delta u= u^{frac{N+2}{N-2}}+varepsilon u, &{}{{text {in}}~Omega }, u>0, &{}{{text {in}}~Omega }, u=0, &{}{text {on}~partial Omega }, end{array}right. } end{aligned}$$</span></div></div><p>where <span>(varepsilon >0)</span> and <span>(Omega subset mathbb {R}^N)</span> are a smooth bounded domain with <span>(Nge 3)</span>. The existence of multi-bump solutions to above problem for small parameter <span>(varepsilon >0)</span> was obtained by Musso and Pistoia (Indiana Univ Math J 51:541–579, 2002). However, to our knowledge, whether the multi-bump solutions are non-degenerate that is open. Here, we give some straightforward answer on this question under some suitable assumptions for the Green’s function of <span>(-Delta )</span> in <span>(Omega )</span>, which enriches the qualitative analysis on the solutions of Brezis-Nirenberg problem and can be viewed as a generalization of Grossi (Nonlinear Differ Equ Appl 12:227–241, 2005) where the non-degeneracy of a single-bump solution has been proved. And the main idea is the blow-up analysis based on the local Pohozaev identities.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 3","pages":"1115 - 1136"},"PeriodicalIF":1.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136317359","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

Hopf type theorems for surfaces in the de Sitter–Schwarzschild and Reissner–Nordstrom manifolds 德西特-施瓦兹柴尔德流形和赖斯纳-诺德斯特罗姆流形中曲面的霍普夫型定理

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2023-10-27 DOI: 10.1007/s10231-023-01384-1

Hilário Alencar, Gregório Silva Neto

引用次数: 0

Compactifications of indefinite 3-Sasaki structures and their quaternionic Kähler quotients 不定3-Sasaki结构的紧凑化及其四元凯勒商数

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2023-10-25 DOI: 10.1007/s10231-023-01385-0

A. Rod Gover, Katharina Neusser, Travis Willse

{"title":"Compactifications of indefinite 3-Sasaki structures and their quaternionic Kähler quotients","authors":"A. Rod Gover, Katharina Neusser, Travis Willse","doi":"10.1007/s10231-023-01385-0","DOIUrl":"10.1007/s10231-023-01385-0","url":null,"abstract":"<div><p>We show that 3-Sasaki structures admit a natural description in terms of projective differential geometry. First we establish that a 3-Sasaki structure may be understood as a projective structure whose tractor connection admits a holonomy reduction, satisfying a particular non-vanishing condition, to the (possibly indefinite) unitary quaternionic group <span>({text {Sp}}(p,q))</span>. Moreover, we show that, if a holonomy reduction to <span>({text {Sp}}(p,q))</span> of the tractor connection of a projective structure does not satisfy this condition, then it decomposes the underlying manifold into a disjoint union of strata including open manifolds with (indefinite) 3-Sasaki structures and a closed separating hypersurface at infinity with respect to the 3-Sasaki metrics. It is shown that the latter hypersurface inherits a Biquard–Fefferman conformal structure, which thus (locally) fibers over a quaternionic contact structure, and which in turn compactifies the natural quaternionic Kähler quotients of the 3-Sasaki structures on the open manifolds. As an application, we describe the projective compactification of (suitably) complete, non-compact (indefinite) 3-Sasaki manifolds and recover Biquard’s notion of asymptotically hyperbolic quaternionic Kähler metrics.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 2","pages":"875 - 902"},"PeriodicalIF":1.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01385-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135113405","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

Variations on average character degrees and solvability 平均字符度和可解性的变化

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2023-10-24 DOI: 10.1007/s10231-023-01393-0

Neda Ahanjideh, Zeinab Akhlaghi, Kamal Aziziheris

{"title":"Variations on average character degrees and solvability","authors":"Neda Ahanjideh, Zeinab Akhlaghi, Kamal Aziziheris","doi":"10.1007/s10231-023-01393-0","DOIUrl":"10.1007/s10231-023-01393-0","url":null,"abstract":"<div><p>Let <i>G</i> be a finite group, <span>(mathbb {F})</span> be one of the fields <span>(mathbb {Q},mathbb {R})</span> or <span>(mathbb {C})</span>, and <i>N</i> be a non-trivial normal subgroup of <i>G</i>. Let <span>({textrm{acd}}^{*}_{{mathbb {F}}}(G))</span> and <span>({textrm{acd}}_{{mathbb {F}}, textrm{even}}(G|N))</span> be the average degree of all non-linear <span>(mathbb {F})</span>-valued irreducible characters of <i>G</i> and of even degree <span>(mathbb {F})</span>-valued irreducible characters of <i>G</i> whose kernels do not contain <i>N</i>, respectively. We assume the average of an empty set is zero for more convenience. In this paper we prove that if <span>(textrm{acd}^*_{mathbb {Q}}(G)< 9/2)</span> or <span>(0<textrm{acd}_{mathbb {Q},textrm{even}}(G|N)<4)</span>, then <i>G</i> is solvable. Moreover, setting <span>(mathbb {F} in {mathbb {R},mathbb {C}})</span>, we obtain the solvability of <i>G</i> by assuming <span>({textrm{acd}}^{*}_{{mathbb {F}}}(G)<29/8)</span> or <span>(0<{textrm{acd}}_{{mathbb {F}}, textrm{even}}(G|N)<7/2)</span>, and we conclude the solvability of <i>N</i> when <span>(0<{textrm{acd}}_{{mathbb {F}}, textrm{even}}(G|N)<18/5)</span>. Replacing <i>N</i> by <i>G</i> in <span>({textrm{acd}}_{{mathbb {F}}, textrm{even}}(G|N))</span> gives us an extended form of a result by Moreto and Nguyen. Examples are given to show that all the bounds are sharp.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"203 3","pages":"1061 - 1092"},"PeriodicalIF":1.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135266466","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

Harmonic almost complex structures on almost abelian Lie groups and solvmanifolds 几乎无差别李群和溶点上的谐波近复结构

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2023-10-24 DOI: 10.1007/s10231-023-01392-1

Adrián Andrada, Alejandro Tolcachier

引用次数: 0

End-point norm estimates for Cesàro and Copson operators Cesàro 和 Copson 算子的端点规范估计值

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2023-10-15 DOI: 10.1007/s10231-023-01390-3

Sorina Barza, Bizuneh M. Demissie, Gord Sinnamon

引用次数: 0

Analysis of a system modeling the interaction between the motion of piston-spring and a viscous gas 活塞弹簧运动与粘性气体相互作用模型系统分析

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2023-10-13 DOI: 10.1007/s10231-023-01386-z

Sabrine Chebbi, Václav Mácha, Šárka Nečasová

引用次数: 0

Sectional nonassociativity of metrized algebras 元化代数的截面非可共性

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2023-10-08 DOI: 10.1007/s10231-023-01372-5

Daniel J. F. Fox

引用次数: 0