Boundary regularity for parabolic systems in convex domains

TL;DR

This paper proves local Lipschitz regularity for solutions to parabolic systems with Uhlenbeck structure in convex domains, extending boundary regularity results up to the lateral boundary under Dirichlet conditions.

Contribution

It establishes boundary regularity estimates for parabolic systems with Uhlenbeck structure in convex domains, a novel extension of interior regularity results.

Findings

Lipschitz estimates hold up to the boundary in convex domains.

Boundary regularity is achieved under homogeneous Dirichlet conditions.

Results apply to weak solutions of parabolic systems with Uhlenbeck structure.

Abstract

In a cylindrical space-time domain with a convex, spatial base, we establish a local Lipschitz estimate for weak solutions to parabolic systems with Uhlenbeck structure up to the lateral boundary, provided homogeneous Dirichlet data are assumed on that part of the lateral boundary.