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

Filippo Cagnetti, Antonin Chambolle, Lucia Scardia

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
30 Downloads (Pure)

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, Poincaré-Korn and Korn inequalities. As an application, we deduce an approximation result which implies the existence of the approximate gradient for displacements in GSBDp.
Original languageEnglish
Pages (from-to)1179–1216
Number of pages38
JournalMathematische Annalen
Volume383
Early online date8 Jun 2021
DOIs
Publication statusPublished - Aug 2022

ASJC Scopus subject areas

  • General Mathematics

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