On Korn-Maxwell-Sobolev Inequalities
Franz Gmeineder, Daniel Spector

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 -norm of a matrix-valued field by the -norm of an elliptic part and the -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 .
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