On Korn-Maxwell-Sobolev Inequalities

Abstract

We establish a family of inequalities that allow one to estimate the $\mathrm{L}^{q}$-norm of a matrix-valued field by the $\mathrm{L}^{q}$-norm of an elliptic part and the $\mathrm{L}^{p}$-norm of the matrix-valued curl. This particularly extends previous work by Neff et al. and, as a main novelty, is applicable in the regime $p=1$.