Maximal Lp – Lq regularity for the quasi-steady elliptic problems

Ken Furukawa; Naoto Kajiwara

doi:10.1007/s00028-020-00638-2

Maximal L_p – L_q regularity for the quasi-steady elliptic problems

Ken Furukawa, Naoto Kajiwara^*

^*Corresponding author for this work

Program of Mathematics and Informatics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we consider maximal regularity for the vector-valued quasi-steady linear elliptic problems. The equations are the elliptic equation in the domain and the evolution equations on its boundary. We prove the maximal L_p–L_q regularity for these problems and give examples that our results are applicable. The Lopatinskii–Shapiro and the asymptotic Lopatinskii–Shapiro conditions are important to get boundedness of solution operators.

Original language	English
Pages (from-to)	1601-1625
Number of pages	25
Journal	Journal of Evolution Equations
Volume	21
Issue number	2
DOIs	https://doi.org/10.1007/s00028-020-00638-2
State	Published - 2021/06

Keywords

Maximal L–L regularity
Quasi-steady problems

ASJC Scopus subject areas

Mathematics (miscellaneous)

Access to Document

10.1007/s00028-020-00638-2

Cite this

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title = "Maximal Lp – Lq regularity for the quasi-steady elliptic problems",

abstract = "In this paper, we consider maximal regularity for the vector-valued quasi-steady linear elliptic problems. The equations are the elliptic equation in the domain and the evolution equations on its boundary. We prove the maximal Lp–Lq regularity for these problems and give examples that our results are applicable. The Lopatinskii–Shapiro and the asymptotic Lopatinskii–Shapiro conditions are important to get boundedness of solution operators.",

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author = "Ken Furukawa and Naoto Kajiwara",

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AB - In this paper, we consider maximal regularity for the vector-valued quasi-steady linear elliptic problems. The equations are the elliptic equation in the domain and the evolution equations on its boundary. We prove the maximal Lp–Lq regularity for these problems and give examples that our results are applicable. The Lopatinskii–Shapiro and the asymptotic Lopatinskii–Shapiro conditions are important to get boundedness of solution operators.

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KW - Quasi-steady problems

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