On Korn's First Inequality for Tangential or Normal Boundary Conditions with Explicit Constants

TL;DR

This paper proves Korn's first inequality with an explicit constant of sqrt(2) for vector fields satisfying boundary conditions on piecewise smooth, concave domains, enhancing understanding of boundary value problems in elasticity.

Contribution

It provides an explicit constant for Korn's first inequality under specific boundary conditions on certain domains, which was previously unknown.

Findings

Korn's first inequality holds with explicit constant sqrt(2)

Applicable to piecewise smooth, concave domains

Results improve bounds for boundary value problems in elasticity

Abstract

We will prove that for piecewise smooth and concave domains Korn's first inequality holds for vector fields satisfying homogeneous normal or tangential boundary conditions with explicit Korn constant square root of 2.