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

Tomasz Piasecki, Yoshihiro Shibata, Ewelina Zatorska

Research output: Contribution to journalArticle


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
JournalJournal of Differential Equations
Publication statusAccepted/In press - 2019 Jan 1


  • Linear parabolic system
  • Maximal regularity
  • R-boundedness

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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