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

Agnid Banerjee*, Prashanta Garain, Juha Kinnunen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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
JournalAnnali di Matematica Pura ed Applicata
DOIs
Publication statusE-pub ahead of print - 15 Nov 2021
MoE publication typeA1 Journal article-refereed

Keywords

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

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