A note on Besov regularity for parabolic initial boundary value problems

TL;DR

This paper investigates the regularity of solutions to the heat equation with Besov space data on Lipschitz domains, leading to improved convergence rates for nonlinear approximation methods.

Contribution

It provides a new regularity exponent for solutions to parabolic problems with Besov data, enhancing approximation techniques.

Findings

Improved regularity exponent for solutions

Enhanced convergence rates for nonlinear approximation methods

Applicability to Lipschitz domain boundary problems

Abstract

In this note we consider the initial boundary value problem for the heat equation on cylinders based on Lipschitz domains with Besov data. We obtain a regularity exponent for the solution that improves the rate of convergence of nonlinear approximation methods.