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July 2020 Maximal $L^{1}$-regularity for parabolic boundary value problems with inhomogeneous data in the half-space
Takayoshi Ogawa, Senjo Shimizu
Proc. Japan Acad. Ser. A Math. Sci. 96(7): 57-62 (July 2020). DOI: 10.3792/pjaa.96.011

Abstract

End-point maximal $L^{1}$-regularity for the parabolic initial-boundary value problem is considered in the half-space. For the inhomogeneous boundary data of both the Dirichlet and the Neumann type, maximal $L^{1}$-regularity for the initial-boundary value problem of parabolic equation is established in time end-point case upon the Besov space as well as the optimal trace estimates. We derive the almost orthogonal properties between the boundary potentials of the Dirichlet and the Neumann boundary data and the Littlewood-Paley dyadic decomposition of unity.

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Takayoshi Ogawa. Senjo Shimizu. "Maximal $L^{1}$-regularity for parabolic boundary value problems with inhomogeneous data in the half-space." Proc. Japan Acad. Ser. A Math. Sci. 96 (7) 57 - 62, July 2020. https://doi.org/10.3792/pjaa.96.011

Information

Published: July 2020
First available in Project Euclid: 17 July 2020

zbMATH: 07244449
MathSciNet: MR4124348
Digital Object Identifier: 10.3792/pjaa.96.011

Subjects:
Primary: 35K20, 42B25

Rights: Copyright © 2020 The Japan Academy

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Vol.96 • No. 7 • July 2020
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