Global regularity for systems with $p$-structure depending on the symmetric gradient

TL;DR

This paper investigates the global regularity of weak solutions to boundary value problems involving systems with p-structure depending solely on the symmetric gradient, providing insights into boundary regularity for such systems.

Contribution

It establishes global regularity results for systems with p-structure depending on the symmetric gradient on smooth bounded domains.

Findings

Proves boundary regularity for weak solutions.

Extends regularity theory to symmetric gradient-dependent systems.

Provides conditions under which solutions are globally regular.

Abstract

In this paper we study on smooth bounded domains the global regularity (up to the boundary) for weak solutions to systems having $p$-structure depending only on the symmetric part of the gradient.