HIGHER REGULARITY FOR PARABOLIC EQUATIONS BASED ON MAXIMAL $L_p$-$L_q$ SPACES
Keywords:
Higher regularity, parabolic equations, maximal $L_p$-$L_q$ regularity.DOI:
https://doi.org/10.17654/0974324322012Abstract
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.
Received: January 4, 2022
Accepted: February 22, 2022
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