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 on 30 Oct 2023



Inserted: 1 may 2023
Last Updated: 30 oct 2023

Year: 2023

ArXiv: 2305.00740 PDF


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.