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Pré-Publication, Document De Travail Année : 2020

KORN AND POINCARÉ-KORN INEQUALITIES FOR FUNCTIONS WITH SMALL JUMP SET

Résumé

In this paper we prove a regularity and rigidity result for displacements in GSBD^p , for every p > 1 and any dimension n ≥ 2. We show that a displacement in GSBD^p with a small jump set coincides with a W^{1,p} function, up to a small set whose perimeter and volume are controlled by the size of the jump. This generalises to higher dimension a result of Conti, Focardi and Iurlano. A consequence of this is that such displacements satisfy, up to a small set, Poincaré-Korn and Korn inequalities. As an application, we deduce an approximation result which implies the existence of the approximate gradient for displacements in GSBD^p.
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Dates et versions

hal-02775095 , version 1 (04-06-2020)
hal-02775095 , version 2 (09-06-2021)

Identifiants

  • HAL Id : hal-02775095 , version 1

Citer

Filippo Cagnetti, Antonin Chambolle, Lucia Scardia. KORN AND POINCARÉ-KORN INEQUALITIES FOR FUNCTIONS WITH SMALL JUMP SET. 2020. ⟨hal-02775095v1⟩
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