Remarks on the maximal regularity for parabolic boundary value problems with inhomogeneous data

TL;DR

This paper extends derivative estimates for solutions to heat equations with boundary data in Besov spaces, covering all derivative orders including fractional derivatives, thus broadening the understanding of maximal regularity in parabolic boundary value problems.

Contribution

It generalizes existing estimates to any order of derivatives, including fractional derivatives, for solutions of heat equations with inhomogeneous boundary data.

Findings

Extended derivative estimates to fractional orders.

Unified approach for all derivative orders.

Enhanced understanding of maximal regularity in parabolic problems.

Abstract

Inspired by Ogawa-Shimizu [JEE 2022] and Chen-Liang-Tsai [IMRN 2025] on the second and first order derivative estimates of solution of heat equation in the upper half space with boundary data in homogeneous Besov spaces, we extend the estimates to any order of derivatives, including fractional derivatives.