On Korn's First Inequality for Mixed Tangential and Normal Boundary Conditions on Bounded Lipschitz-Domains in $\mathbb{R}^N$

TL;DR

This paper proves Korn's first inequality for vector fields with mixed boundary conditions on bounded Lipschitz domains in any dimension, extending its applicability in mathematical analysis and PDEs.

Contribution

It establishes Korn's first inequality under mixed boundary conditions on Lipschitz domains, a significant extension of previous results.

Findings

Korn's first inequality holds for mixed boundary conditions

Valid on bounded Lipschitz domains in $\

Applicable to vector fields with normal and tangential boundary conditions

Abstract

We prove that for bounded Lipschitz domains in $\mathbb{R}^N$ Korn's first inequality holds for vector fields satisfying homogeneous mixed normal and tangential boundary conditions.