On the regularity theory for mixed local and nonlocal quasilinear parabolic equations

Prashanta Garain, Juha Kinnunen

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)
6 Downloads (Pure)

Abstract

We consider mixed local and nonlocal quasilinear parabolic equations of p-Laplace type and discuss several regularity properties of weak solutions for such equations. More precisely, we establish local boundedness of weak subsolutions, lower semicontinuity of weak supersolutions as well as upper semicontinuity of weak subsolutions. We also discuss the pointwise behavior of the semicontinuous representatives. Our main results are valid for sign-changing solutions. Our approach is purely analytic and is based on energy estimates and the De Giorgi theory.
Original languageEnglish
Pages (from-to)495-541
Number of pages47
JournalAnnali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume25
Issue number1
DOIs
Publication statusPublished - 31 Mar 2024
MoE publication typeA1 Journal article-refereed

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