On the maximal Lp-Lq regularity of solutions to a general linear parabolic system

Tomasz Piasecki*, Yoshihiro Shibata, Ewelina Zatorska

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We show the existence of solution in the maximal Lp−Lq regularity framework to a class of symmetric parabolic problems on a uniformly C2 domain in Rn. Our approach consist in showing R - boundedness of families of solution operators to corresponding resolvent problems first in the whole space, then in half-space, perturbed half-space and finally, using localization arguments, on the domain. Assuming additionally boundedness of the domain we also show exponential decay of the solution. In particular, our approach does not require assuming a priori the uniform Lopatinskii - Shapiro condition.

Original languageEnglish
Pages (from-to)3332-3369
Number of pages38
JournalJournal of Differential Equations
Issue number7
Publication statusPublished - 2020 Mar 15


  • Linear parabolic system
  • Maximal regularity
  • R-boundedness

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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