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

Filippo Cagnetti, Antonin Chambolle, Lucia Scardia

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
10 Downloads (Pure)


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
JournalMathematische Annalen
Early online date8 Jun 2021
Publication statusE-pub ahead of print - 8 Jun 2021

ASJC Scopus subject areas

  • Mathematics(all)


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