HIGHER REGULARITY FOR PARABOLIC EQUATIONS BASED ON MAXIMAL Lp-Lq SPACES

Naoto Kajiwara

Naoto Kajiwara Applied Physics Course, Department of Electrical,Electronic and Computer Engineering Gifu University, 1-1 Yanagido Gifu, Gifu, 501-1193, Japan

Article ID: 2549

Keywords: Higher regularity; parabolic equations; maximal Lp-Lq regularity

Abstract

In this paper, we prove higher regularity for 2mth order parabolic equations with general boundary conditions. This is a kind of maximal Lp-Lq 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.

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