Korn and Poincare-Korn inequalities for functions with a small jump set

Cagnetti, Filippo, Chambolle, Antonin and Scardia, Lucia (2021) Korn and Poincare-Korn inequalities for functions with a small jump set. Mathematische Annalen. ISSN 0025-5831

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Abstract

In this paper we prove a regularity and rigidity result for displacements in GSBDp, for every p > 1 and any dimension n ≥ 2. We show that a displacement in GSBDp with a small jump set coincides with a W1,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, Poincar´e-Korn and Korn inequalities. As an application, we deduce an approximation result which implies the existence of the approximate gradient for displacements in GSBDp.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 20 May 2021 06:57
Last Modified: 17 Jun 2021 09:30
URI: http://sro.sussex.ac.uk/id/eprint/99257

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