Geometric rigidity on Sobolev spaces with variable exponent and applications

被引：1

作者：

Almi, Stefano ^{[1
,4
]}

Caponi, Maicol ^{[1
]}

Friedrich, Manuel ^{[2
,3
]}

Solombrino, Francesco ^{[1
]}

机构：

[1] Univ Naples Federico II, Dept Math & Applicat R Caccioppoli, Via Cintia, I-80126 Naples, Italy

[2] Friedrich Alexander Univ Erlangen Nurnberg, Dept Math, Cauerstr 11, D-91058 Erlangen, Germany

[3] Univ Munster, Math Munster, Einsteinstr 62, D-48149 Munster, Germany

[4] Univ Aquila, Dept Informat Engn Comp Sci & Math, Via Vetoio 1, I-67100 Laquila, Italy

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2025年 / 32卷 / 01期

基金：

奥地利科学基金会;

关键词：

Rigidity estimates; Korn inequality; Variable exponent; Mixed growth; Nonlinear and linear elasticity; Gamma-convergence; GAMMA-LIMIT; NONLINEAR ELASTICITY; GRIFFITH ENERGIES; LINEAR ELASTICITY; INEXTENSIBLE RODS; DERIVATION; REGULARITY; CONVERGENCE; MINIMIZERS; MODELS;

D O I：

10.1007/s00030-024-01016-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present extensions of rigidity estimates and of Korn's inequality to the setting of (mixed) variable exponents growth. The proof techniques, based on a classical covering argument, rely on the log-Holder continuity of the exponent to get uniform regularity estimates on each cell of the cover, and on an extension result a la Nitsche in Sobolev spaces with variable exponents. As an application, by means of Gamma-convergence we perform a passage from nonlinear to linearized elasticity under variable subquadratic energy growth far from the energy well.

引用

页数：50

共 50 条

[21] Variable Exponent Sobolev Spaces for Semilinear Elliptic Systems
Zhong Tan
Fei Fang
Mediterranean Journal of Mathematics, 2013, 10 : 1353 - 1367
[22] VARIABLE EXPONENT SOBOLEV SPACES ASSOCIATED WITH JACOBI EXPANSIONS
Almeida, Victor
Betancor, Jorge J.
Castro, Alejandro J.
Sanabria, Alejandro
Scotto, Roberto
JOURNAL OF MATHEMATICAL INEQUALITIES, 2017, 11 (04): : 901 - 946
[23] On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications
Chems Eddine, Nabil
Ragusa, Maria Alessandra
Repovs, Dusan D.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2024, 27 (02) : 725 - 756
[24] On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications
Nabil Chems Eddine
Maria Alessandra Ragusa
Dušan D. Repovš
Fractional Calculus and Applied Analysis, 2024, 27 : 725 - 756
[25] Modular Geometric Properties in Variable Exponent Spaces
Khamsi, Mohamed A.
Mendez, Osvaldo D.
Reich, Simeon
MATHEMATICS, 2022, 10 (14)
[26] Variable Exponent p(middot)-Kirchhoff Type Problem with Convection in Variable Exponent Sobolev Spaces
El Hammar, Hasnae
El Ouaarabi, Mohamed
Allalou, Chakir
Melliani, Said
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2023, 41 : 19 - 19
[27] On the Sobolev trace Theorem for variable exponent spaces in the critical range
Fernandez Bonder, Julian
Saintier, Nicolas
Silva, Analia
ANNALI DI MATEMATICA PURA ED APPLICATA, 2014, 193 (06) : 1607 - 1628
[28] Embedding theorems for variable exponent fractional Sobolev spaces and an application
Liu, Haikun
Fu, Yongqiang
AIMS MATHEMATICS, 2021, 6 (09): : 9835 - 9858
[29] CHARACTERIZATIONS OF SOBOLEV SPACES WITH VARIABLE EXPONENT VIA AVERAGES ON BALLS
Xu, Jingshi
TOHOKU MATHEMATICAL JOURNAL, 2020, 72 (04) : 569 - 579
[30] Counter-examples of regularity in variable exponent Sobolev spaces
Hästö, PA
P-HARMONIC EQUATION AND RECENT ADVANCES IN ANALYSIS, 2005, 370 : 133 - +

← 1 2 3 4 5 →