In this paper, we prove higher regularity for 2mth 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 condition for the initial data. As a corollary, we are able to get a unique smooth solution if the data satisfying compatibility conditions are smooth.

Higher regularity, parabolic equations, maximal L_p-L_q regularity.

Received: January 4, 2022; Accepted: February 22, 2022; Published: March 2, 2022

How to cite this article: Naoto Kajiwara, Higher regularity for parabolic equations based on maximal  spaces, Advances in Differential Equations and Control Processes 27 (2022), 55-71. http://dx.doi.org/10.17654/0974324322012

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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