A nonlinear Korn inequality based on the Green-Saint Venant strain tensor

TL;DR

This paper proves a nonlinear Korn inequality involving the Green-Saint Venant strain tensor for displacements in Sobolev spaces, which aids in establishing coercivity of nonlinear elastic energies.

Contribution

It introduces a new nonlinear Korn inequality based on the Green-Saint Venant strain tensor for Sobolev space displacements with boundary conditions.

Findings

Establishment of a nonlinear Korn inequality for Sobolev displacements.

Application potential in proving coercivity of nonlinear elastic energy.

Theoretical advancement in nonlinear elasticity analysis.

Abstract

A nonlinear Korn inequality based on the Green-Saint Venant strain tensor is proved, whenever the displacement is in the Sobolev space $W^{1,p}$, $p\geq 2$, under Dirichlet conditions on a part of the boundary. The inequality can be useful in proving the coercivity of a nonlinear elastic energy.