Some local properties of subsolution and supersolutions for a doubly nonlinear nonlocal p-Laplace equation

Agnid Banerjee, Prashanta Garain, Juha Kinnunen

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We establish a local boundedness estimate for weak subsolutions to a doubly nonlinear parabolic fractional p-Laplace equation. Our argument relies on energy estimates and a parabolic nonlocal version of De Giorgi’s method. Furthermore, by means of a new algebraic inequality, we show that positive weak supersolutions satisfy a reverse Hölder inequality. Finally, we also prove a logarithmic decay estimate for positive supersolutions.

Original languageEnglish
Pages (from-to)1717-1751
Number of pages35
JournalAnnali di Matematica Pura ed Applicata
Volume201
Issue number4
DOIs
StatePublished - 1 Aug 2022
Externally publishedYes

Keywords

  • De Giorgi’s method
  • Doubly nonlinear parabolic equation
  • Energy estimates
  • Fractional p-Laplace equation

ASJC Scopus subject areas

  • Applied Mathematics

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