Calculus of Variations and Geometric Measure Theory

S. Almi - M. Caponi - M. Friedrich - F. Solombrino

Geometric rigidity on Sobolev spaces with variable exponent and applications

created by caponi on 01 May 2023
modified by solombrino on 27 Nov 2024

[BibTeX]

Accepted Paper

Inserted: 1 may 2023
Last Updated: 27 nov 2024

Journal: Nonlinear Differential Equations and Applications
Year: 2023

ArXiv: 2305.00740 PDF

Abstract:

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-Hölder continuity of the exponent to get uniform regularity estimates on each cell of the cover, and on an extension result à 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.


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