Calculus of Variations and Geometric Measure Theory

F. Cagnetti - A. Chambolle - M. Perugini - L. Scardia

An extension result for generalised special functions of bounded deformation

created by cagnetti on 02 Jun 2020
modified by perugini on 17 Jan 2021


Published Paper

Inserted: 2 jun 2020
Last Updated: 17 jan 2021

Journal: J. Convex Anal.
Year: 2021


We show an extension result for functions in $GSBD^p$, for every $p>1$ and any dimension $n\geq 2$. The proof is based on a recent result in $[7]$, where it is shown that a function $u$ in $GSBD^p$ with a "small" jump set coincides with a $W^{1,p}$ function, up to a small set whose perimeter and volume are controlled by the size of the jump of $u$.