Higher regularity for parabolic equations based on maximal L_p-L_q spaces
Analysis of PDEs
2020-11-24 v1
Abstract
In this paper we prove higher regularity for 2m-th order parabolic equations with general boundary conditions. This is a kind of maximal L_p-L_q regularity with differentiability, i.e. the main theorem is isomorphism between the solution space and the data space using Besov and Triebel--Lizorkin spaces. The key is compatibility conditions for the initial data. We are able to get a unique smooth solution if the data satisfying compatibility conditions are smooth.
Keywords
Cite
@article{arxiv.2011.10964,
title = {Higher regularity for parabolic equations based on maximal L_p-L_q spaces},
author = {Naoto Kajiwara},
journal= {arXiv preprint arXiv:2011.10964},
year = {2020}
}