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

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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2024-03-31

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en

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47

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Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Volume 25, issue 1, pp. 495-541

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.

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Publisher Copyright: © 2024 Scuola Normale Superiore. All rights reserved.

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Garain, P & Kinnunen, J 2024, ' On the regularity theory for mixed local and nonlocal quasilinear parabolic equations ', Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, vol. 25, no. 1, pp. 495-541 . https://doi.org/10.2422/2036-2145.202110_006