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

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