Parabolic problems with general Wentzell boundary conditions and diffusion on the boundary

TL;DR

This paper establishes maximal regularity results for linear parabolic systems with Wentzell boundary conditions, including boundary diffusion, in H"older spaces, advancing the understanding of such boundary value problems.

Contribution

It provides new maximal regularity results for parabolic systems with general Wentzell boundary conditions involving boundary diffusion.

Findings

Maximal regularity in H"older spaces for parabolic systems with Wentzell boundary conditions.

Extension of regularity theory to include boundary diffusion terms.

Applicable to linear parabolic systems with dynamic boundary conditions.

Abstract

We show a result of maximal regularity in spaces of H\"older continuous function, concerning linear parabolic systems, with dynamic or Wentzell boundary conditions, with an elliptic diffusion term on the boundary.