A method for obtaining time-periodic Lp estimates

Mads Kyed*, Jonas Sauer

*この研究の対応する著者

研究成果: Article査読

6 被引用数 (Scopus)

抄録

We introduce a method for showing a priori Lp estimates for time-periodic, linear, partial differential equations set in a variety of domains such as the whole space, the half space and bounded domains. The method is generic and can be applied to a wide range of problems. We demonstrate it on the heat equation. The main idea is to replace the time axis with a torus in order to reformulate the problem on a locally compact abelian group and to employ Fourier analysis on this group. As a by-product, maximal Lp regularity for the corresponding initial-value problem follows without the notion of R-boundedness. Moreover, we introduce the concept of a time-periodic fundamental solution.

本文言語English
ページ(範囲)633-652
ページ数20
ジャーナルJournal of Differential Equations
262
1
DOI
出版ステータスPublished - 2017 1月 5
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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