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.
Geometric rigidity on Sobolev spaces with variable exponent and applications
Caponi, Maicol
;
2025-01-01
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.File in questo prodotto:
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