Korn-Poincarè inequalities for functions with a small jump set (Q2833074)

Korn-Poincaré's inequality concerns an \(L^p\) estimation of a function \(u(x)\) (defined in some regular domain \(\Omega\subset\mathbb R^n\)) with an affine function \(Ax+b\), using the \(L^p\) norm of the skew-symmetric part of the gradient of \(u\). The article under review brings a result of this type in the setting of functions of so-called special bounded deformation. The setting allows a non-zero jump part in the decomposition of \(u\), with the \(L^p\)-estimation taken away from the jump set of \(u\).