Geometric rigidity on Sobolev spaces with variable exponent and applications

Almi S, Caponi M, Friedrich M, Solombrino F (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Nodea-Nonlinear Differential Equations and Applications Springer Verlag (Germany)

Book Volume: 32

Article Number: 12

Journal Issue: 1

DOI: 10.1007/s00030-024-01016-4

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 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.

Authors with CRIS profile

Manuel Friedrich Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

Università degli Studi di Napoli Federico II IT Italy (IT)

How to cite

APA:

Almi, S., Caponi, M., Friedrich, M., & Solombrino, F. (2025). Geometric rigidity on Sobolev spaces with variable exponent and applications. Nodea-Nonlinear Differential Equations and Applications, 32(1). https://doi.org/10.1007/s00030-024-01016-4

MLA:

Almi, Stefano, et al. "Geometric rigidity on Sobolev spaces with variable exponent and applications." Nodea-Nonlinear Differential Equations and Applications 32.1 (2025).

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