TY - JOUR
T1 - Korn and Poincaré-Korn inequalities for functions with a small jump set
AU - Cagnetti, Filippo
AU - Chambolle, Antonin
AU - Scardia, Lucia
N1 - Funding Information:
The authors would like to thank the referee for carefully reading the manuscript and for providing several helpful suggestions. The authors acknowledge the hospitality and support of the INI under the Grant EP/R014604/1.
Publisher Copyright:
© 2021, The Author(s).
PY - 2021/6/8
Y1 - 2021/6/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85107734267&partnerID=8YFLogxK
U2 - 10.1007/s00208-021-02210-w
DO - 10.1007/s00208-021-02210-w
M3 - Article
SN - 0025-5831
JO - Mathematische Annalen
JF - Mathematische Annalen
ER -