On Korn-Maxwell-Sobolev Inequalities

TL;DR

This paper introduces a new family of Korn-Maxwell-Sobolev inequalities that estimate matrix field norms using elliptic and curl components, notably extending applicability to the case where p=1.

Contribution

It extends previous inequalities to include the case p=1, broadening the scope of matrix field norm estimates in mathematical analysis.

Findings

Established inequalities for matrix-valued fields involving elliptic and curl components.

Extended the applicability of Korn-Maxwell-Sobolev inequalities to the p=1 regime.

Generalized previous results by Neff et al. to a wider range of p-values.

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 $p=1$.