A method for obtaining time-periodic Lp estimates

Mads Kyed*, Jonas Sauer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2017 Jan 5
Externally publishedYes


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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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