Rendiconti Lincei-Matematica e Applicazioni最新文献_第3页

Internal mode-induced growth in $3$d nonlinear Klein–Gordon equations $3$d非线性Klein-Gordon方程的内模诱导增长

IF 0.5 4区数学

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2022-03-11 DOI: 10.4171/rlm/986

Tristan L'eger, F. Pusateri

引用次数: 3

Closed selections of Vitali’s type Vitali类型的封闭式选择

IF 0.5 4区数学

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2022-02-21 DOI: 10.4171/rlm/956

Jeremy Mirmina, D. Puglisi

引用次数: 1

Non-homogeneous Dirichlet problems with concave-convex reaction 具有凹凸反应的非齐次Dirichlet问题

IF 0.5 4区数学

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2022-02-21 DOI: 10.4171/rlm/959

G. Bonanno, R. Livrea, Vicentiu D. Rădulescu, A. Ambrosetti

引用次数: 0

$Gamma$-Stability of maximal monotone processes $Gamma$-极大单调过程的稳定性

IF 0.5 4区数学

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2022-02-21 DOI: 10.4171/rlm/951

A. Visintin

引用次数: 0

Carleson estimates for the singular parabolic $p$-Laplacian in time-dependent domains 时变域奇异抛物-拉普拉斯算子的Carleson估计

IF 0.5 4区数学

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2022-02-21 DOI: 10.4171/rlm/953

U. Gianazza

引用次数: 0

A multiplicity theorem for anisotropic Robin equations 各向异性Robin方程的多重性定理

IF 0.5 4区数学

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2022-02-15 DOI: 10.4171/rlm/961

Nikolaos S. Papageorgiou, Patrick Winkert

引用次数: 0

Sobolev spaces revisited 索博列夫空间重新审视

IF 0.5 4区数学

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2022-02-03 DOI: 10.4171/RLM/976

H. Brezis, A. Seeger, Jean Van Schaftingen, Po-Lam Yung

引用次数: 12

Uniqueness of the critical point for solutions of some p-Laplace equations in the plane 平面上某些p-拉普拉斯方程解的临界点的唯一性

IF 0.5 4区数学

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2022-01-30 DOI: 10.4171/rlm/997

William Borrelli, S. Mosconi, M. Squassina

引用次数: 3

On the analyticity of the Dirichlet–Neumann operator and Stokes waves 关于Dirichlet–Neumann算子和Stokes波的分析性

IF 0.5 4区数学

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2022-01-12 DOI: 10.4171/rlm/983

M. Berti, A. Maspero, Paolo Ventura

引用次数: 2

Sobolev-type regularity and Pohozaev-type identities for some degenerate and singular problems 一些退化和奇异问题的sobolev型正则性和pohozaev型恒等式

IF 0.5 4区数学

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2022-01-09 DOI: 10.4171/rlm/980

V. Felli, Giovanni Siclari

{"title":"Sobolev-type regularity and Pohozaev-type identities for some degenerate and singular problems","authors":"V. Felli, Giovanni Siclari","doi":"10.4171/rlm/980","DOIUrl":"https://doi.org/10.4171/rlm/980","url":null,"abstract":"on the bottom of a half (N + 1)-dimensional ball. The interest in such a type of equations and related regularity issues has developed starting from the pioneering paper [7], proving local Hölder continuity results and Harnack’s inequalities, and has grown significantly in recent years stimulated by the study of the fractional Laplacian in its realization as a Dirichlet-to-Neumann map [3]. In this context, among recent regularity results for problems of type (1)–(2), we mention [2] and [12] for Schauder and gradient estimates with A being the identity matrix and c ≡ 0. More general degenerate/singular equations of type (1), admitting a varying coefficient matrix A, are considered in [19, 20]. In [19], under suitable regularity assumptions on A and c, Hölder continuity and C-regularity are established for solutions to (1)–(2) in the case h ≡ g ≡ 0, which, up to a reflection through the hyperspace t = 0, corresponds to the study of solutions to the equation − div(|t|1−2sA∇U) + |t|1−2sc = 0 which are even with respect to the t-variable; Hölder continuity of solutions which are odd in t is instead investigated in [20]. In addition, in [19] C and C bounds are derived for some inhomogeneous Neumann boundary problems (i.e. for g 6≡ 0) in the case c ≡ 0. The goal of the present note is to derive Sobolev-type regularity results for solutions to (1)–(2). Under suitable assumptions on c, h, g, the presence of the singular/degenerate homogenous weight, involving only the (N +1)-th variable t, makes the solutions to have derivates with respect to the first N variables x1, x2, . . . , xN belonging to a weighted H -space (with the same weight t1−2s); concerning the regularity of the derivative with respect to t, we obtain instead that the weighted derivative t1−2s ∂U ∂t belongs to a H-space with the dual weight t2s−1, confirming what has already been observed in [19, Lemma 7.1] for even solutions of the reflected problem corresponding to (1)–(2) with h ≡ g ≡ 0.","PeriodicalId":54497,"journal":{"name":"Rendiconti Lincei-Matematica e Applicazioni","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48182046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2