Maximal L1-regularity for parabolic boundary value problems with inhomogeneous data in the half-space

Takayoshi OGAWA, Senjo Shimizu

Research output: Contribution to journalArticlepeer-review

Abstract

End-point maximal L1-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 L1-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.

Original languageEnglish
Pages (from-to)57-62
Number of pages6
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Volume96
Issue number7
DOIs
Publication statusPublished - 2020 Jul

Keywords

  • Maximal L1-regularity end-point estimate initial-boundary value problem
  • the Dirichlet problem the Neumann problem

ASJC Scopus subject areas

  • Mathematics(all)

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