A method for obtaining time-periodic Lp estimates

Mads Kyed, Jonas Sauer

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)633-652
Number of pages20
JournalJournal of Differential Equations
Volume262
Issue number1
DOIs
Publication statusPublished - 2017 Jan 5
Externally publishedYes

Keywords

  • A priori estimates
  • Heat equation
  • Maximal regularity
  • Time-periodic

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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