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

A curvature varifold whose weak second fundamental form is not preserved under decompositions 在分解下不保持弱第二基本形式的曲率变量

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-08-20 DOI: 10.1007/s10231-025-01601-z

Nicolau S. Aiex

引用次数: 0

Boundedness, ultracontractive bounds and optimal evolution of the support for doubly nonlinear anisotropic diffusion 双非线性各向异性扩散支撑的有界性、超收缩界及最优演化

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-08-14 DOI: 10.1007/s10231-025-01600-0

Simone Ciani, Vincenzo Vespri, Matias Vestberg

{"title":"Boundedness, ultracontractive bounds and optimal evolution of the support for doubly nonlinear anisotropic diffusion","authors":"Simone Ciani, Vincenzo Vespri, Matias Vestberg","doi":"10.1007/s10231-025-01600-0","DOIUrl":"10.1007/s10231-025-01600-0","url":null,"abstract":"<div><p>We investigate some regularity properties of a class of doubly nonlinear anisotropic evolution equations whose model case is </p><div><div><span>$$begin{aligned} partial _t big (|u|^{alpha -1}u big ) - sum ^N_{i=1} partial _i big ( |partial _i u|^{p_i - 2} partial _i u big ) = 0, end{aligned}$$</span></div></div><p>where <span>(alpha > 0)</span> and <span>(p_i in (1, infty ))</span>. We obtain super and ultracontractive bounds, and global boundedness in space for solutions to the Cauchy problem with initial data in <span>(L^{alpha +1}(mathbb {R}^N))</span>, and show that the mass is nonincreasing over time. As a consequence, compactly supported evolution is shown for optimal exponents. We introduce a seemingly new paradigm, by showing that Caccioppoli estimates, local boundedness and semicontinuity are consequences of the membership to a suitable energy class. This membership is proved by first establishing the continuity of the map <span>(t mapsto |u|^{alpha -1}u(cdot ,t) in L^{1+1/alpha }_{text {loc}}(Omega ))</span> permitting us to use a suitable mollified weak formulation along with an appropriate test function.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 1","pages":"181 - 231"},"PeriodicalIF":0.9,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-025-01600-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579649","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

Multiplicity of solutions for singular fractional (1)-Laplacian problems: an approximation approach 奇异分数阶(1) -拉普拉斯问题解的多重性：一种近似方法

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-08-13 DOI: 10.1007/s10231-025-01602-y

Aldo Henrique de Souza Medeiros, Gilberto Assis Pereira, Jeferson Camilo Silva

{"title":"Multiplicity of solutions for singular fractional (1)-Laplacian problems: an approximation approach","authors":"Aldo Henrique de Souza Medeiros, Gilberto Assis Pereira, Jeferson Camilo Silva","doi":"10.1007/s10231-025-01602-y","DOIUrl":"10.1007/s10231-025-01602-y","url":null,"abstract":"<div><p>In this paper, we investigate a class of problems involving the fractional <span>(1)</span>-Laplacian operator in general Lipschitz domains, addressing both singular and superlinear nonlinearities. We establish the existence of at least two distinct positive weak solutions. The singular term, combined with the norm in the fractional Sobolev space <span>(W^{s,1}(Omega ))</span>, renders the associated energy functional non-differentiable. This non-differentiability precludes the direct application of variational methods to obtain solutions as critical points in the space <span>(W^{s,1}(Omega ))</span>. To address this challenge, we employ an approximation scheme that involves an auxiliary problem with the fractional <span>(p)</span>-Laplacian operator, where <span>(p > 1)</span>. By deriving uniform estimates, we allow <span>(p)</span> to approach <span>(1)</span>, thereby constructing solutions for the original problem. It is worth emphasizing that the lack of a compact embedding between the relevant function spaces <span>(W_0^{s,p}(Omega ))</span> and <span>(W_0^{s,q}(Omega ))</span> with <span>(p ne q)</span> introduces significant difficulties to our analysis. Additionally, the absence of the validity of Hölder and Young inequalities in this fractional context further complicates the problem. Finally, unlike the case of classical (non-fractional) Sobolev spaces, it is not known whether the Sobolev constant <span>(S_{s,p})</span> converges to <span>(S_{s,1})</span> as <span>(p rightarrow 1^{+})</span>, which necessitates working with bounding constants instead.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 1","pages":"247 - 280"},"PeriodicalIF":0.9,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579521","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

The Hartogs-Bochner extension for monogenic functions of several vector variables and the Dirac complex 若干矢量变量单基因函数的Hartogs-Bochner推广及Dirac复形

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-08-08 DOI: 10.1007/s10231-025-01599-4

Yun Shi, Wei Wang

{"title":"The Hartogs-Bochner extension for monogenic functions of several vector variables and the Dirac complex","authors":"Yun Shi, Wei Wang","doi":"10.1007/s10231-025-01599-4","DOIUrl":"10.1007/s10231-025-01599-4","url":null,"abstract":"<div><p>Holomorphic functions in several complex variables were generalized to regular functions in several quaternionic variables, and further to monogenic functions of several vector variables, which are annihilated by several Dirac operators on <i>k</i> copies of the Euclidean space <span>({mathbb {R}}^n)</span>. As the Dolbeault complex in complex analysis, the Dirac complex resolving several Dirac operators plays the fundamental role to investigate monogenic functions. Although the spaces in the Dirac complex are complicated irreducible modules of <span>(textrm{GL}(k)times textrm{Spin}(n),)</span> we give a simple characterization of the first four spaces, which allows us to write down first three operators in the Dirac complex explicitly and to show this part to be an elliptic complex. Then the PDE method can be applied to obtain solutions to the non-homogeneous several Dirac equations under the compatibility condition, which implies the Hartogs’ phenomenon for monogenic functions. Moreover, we find the boundary version of several Dirac operators and introduce the notion of a tangentially monogenic function, corresponding to tangential Cauchy-Riemann operator and CR functions in several complex variables, and establish the Hartogs-Bochner extension for tangentially monogenic functions on the boundary of a domain.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 1","pages":"147 - 179"},"PeriodicalIF":0.9,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-025-01599-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579163","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

Optimal bounds for the first eigenvalue of fourth-order beam equations with integrable potentials 具有可积势的四阶束方程第一特征值的最优界

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-07-17 DOI: 10.1007/s10231-025-01592-x

Yongkang Cheng, Gang Meng, Zhi Qian

引用次数: 0

A connection between minimal surfaces and the two-dimensional analogues of a problem of Euler 最小曲面与二维欧拉问题之间的一种联系

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-07-16 DOI: 10.1007/s10231-025-01593-w

Rafael López

引用次数: 0

Semi-linear optimal control problems with strong contrasting diffusivity in rough domains 粗糙域上具有强对比扩散性的半线性最优控制问题

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-07-15 DOI: 10.1007/s10231-025-01594-9

A. K. Nandakumaran, Abu Sufian, Renjith Thazhathethil

引用次数: 0

Symmetry of propagation of Fisher-KPP equations: random dispersal v.s. nonlocal dispersal Fisher-KPP方程传播的对称性：随机扩散与非局部扩散

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-07-15 DOI: 10.1007/s10231-025-01591-y

Tao Zhou

{"title":"Symmetry of propagation of Fisher-KPP equations: random dispersal v.s. nonlocal dispersal","authors":"Tao Zhou","doi":"10.1007/s10231-025-01591-y","DOIUrl":"10.1007/s10231-025-01591-y","url":null,"abstract":"<div><p>In this paper, we investigate the properties of spreading speeds of the following Fisher-KPP equation in almost periodic media: </p><div><div><span>$$begin{aligned} left{ begin{aligned} u_t(t,x)=mathcal {M}u(t,x)+f(x,u(t,x)), t>0, xin mathbb {R}, u(0,x)ge 0, u(0,cdot )ne 0 text {with compact support,} end{aligned} right. end{aligned}$$</span></div></div><p>where either <span>(mathcal {M}u(t,x)=mathcal {M}^ru(t,x):=partial _x(a(x)partial _{x}u(t,x))+b(x)partial _{x}u(t,x))</span>, which represents the random dispersal, or <span>(mathcal {M}u(t,x)=mathcal {M}^nu(t,x):=int _{mathbb {R}}big (u(t,x-y)-u(t,x)big )dmu (y))</span>, which represents the nonlocal dispersal. With the existence of the spreading speeds <span>(omega ^pm )</span> in the positive and negative directions of the equation at hand, we 1. give a sufficient and necessary condition for <span>(omega ^+=omega ^-)</span>, which means that the propagation of the solution is symmetric when <span>(mathcal {M}=mathcal {M}^r)</span>; 2. illustrate that the condition above is a sufficient but not necessary one when <span>(mathcal {M}=mathcal {M}^n)</span>; 3. give some other sufficient conditions for <span>(omega ^+=omega ^-)</span> when <span>(mathcal {M}=mathcal {M}^n.)</span></p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 6","pages":"2779 - 2796"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580645","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

Geometric inequalities for quasi-Einstein manifolds 拟爱因斯坦流形的几何不等式

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-07-15 DOI: 10.1007/s10231-025-01595-8

Rafael Diógenes, Jaciane Gonçalves, Ernani Ribeiro Jr

引用次数: 0

Streets-Tian Conjecture on several special types of Hermitian manifolds 几种特殊类型厄米流形的Streets-Tian猜想

IF 0.9 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-07-14 DOI: 10.1007/s10231-025-01597-6

Yuqin Guo, Fangyang Zheng

{"title":"Streets-Tian Conjecture on several special types of Hermitian manifolds","authors":"Yuqin Guo, Fangyang Zheng","doi":"10.1007/s10231-025-01597-6","DOIUrl":"10.1007/s10231-025-01597-6","url":null,"abstract":"<div><p>A Hermitian-symplectic metric is a Hermitian metric whose Kähler form is given by the (1, 1)-part of a closed 2-form. Streets-Tian Conjecture states that a compact complex manifold admitting a Hermitian-symplectic metric must be Kählerian (i.e., admitting a Kähler metric). The conjecture is known to be true in complex dimension 2 but is still open in complex dimensions 3 or higher. In this article, we confirm the conjecture for some special types of compact Hermitian manifolds, including Chern Kähler-like manifolds, non-balanced Bismut torsion parallel (BTP) manifolds, and compact quotients of Lie groups whose Lie algebra contains a <i>J</i>-invariant abelian ideal of codimension 2. The last type is a natural generalization to (compact quotients of) almost abelian Lie groups. The non-balanced BTP case contains all Vaisman manifolds and all Bismut Kähler-like manifolds as subsets. These results extend some of the earlier works on the topic by Fino, Kasuya, Vezzoni, Angella, Otiman, Paradiso, and others. Our approach is elementary in nature, by giving explicit descriptions of Hermitian-symplectic metrics on such spaces as well as the pathways of deforming them into Kähler ones, aimed at illustrating the algebraic complexity and subtlety of Streets-Tian Conjecture.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"205 1","pages":"101 - 118"},"PeriodicalIF":0.9,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147579171","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