Higher regularity for parabolic equations based on maximal L_p-L_q spaces

2020/11/22 by Kajiwara, Naoto
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.10964

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.

Related

• \L_p-maximal regularity for parabolic and elliptic boundary\n value problems with boundary conditions of mixed differentiability orders
• Second-order regularity for parabolic p-Laplace problems
• Second Order Operators Subject to Dirichlet Boundary Conditions in Weighted Triebel-Lizorkin Spaces: Parabolic Problems
• Maximal Regularity with Weights for Parabolic Problems with\n Inhomogeneous Boundary Conditions
• On the maximal L_p-L_q regularity of solutions to a general linear parabolic system