Cagnetti2021_Article_KornAndPoincaré-KornInequaliti.pdf (590.33 kB)
Korn and Poincare-Korn inequalities for functions with a small jump set
Version 2 2023-06-12, 09:52
Version 1 2023-06-09, 23:54
journal contribution
posted on 2023-06-12, 09:52 authored by Filippo Cagnetti, Antonin Chambolle, Lucia ScardiaIn 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.
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Mathematische AnnalenISSN
0025-5831Publisher
SpringerExternal DOI
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2021-05-20First Open Access (FOA) Date
2021-06-17First Compliant Deposit (FCD) Date
2021-05-19Usage metrics
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