Geometric rigidity on Sobolev spaces with variable exponent and applications - Almi, Stefano; Caponi, Maicol; Friedrich, Manuel; Solombrino, Francesco (Nodea-Nonlinear Differential Equations and Applications, 2025)
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 laNitsche in Sobolev spaces with variable exponents. As an application, by means of Γ-convergence we perform a passage from nonlinear to linearized elasticity under variable subquadratic energy growth far from the energy well.
CRIS-Team Scopus Importer:2025-02-17
Keywords: Korn inequality; Mixed growth; Nonlinear and linear elasticity; Rigidity estimates; Variable exponent; Γ-convergence