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arXiv · 2011.10964

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

Naoto Kajiwara
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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.

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Naoto Kajiwara. 2020-11-22. Higher regularity for parabolic equations based on maximal L_p-L_q spaces. https://arxiv.org/abs/2011.10964

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