Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic p-Laplace equations

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2023-10-01
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Mcode
Degree programme
Language
en
Pages
Series
Communications in Contemporary Mathematics, articlenumber 2250032
Abstract
We discuss pointwise behavior of weak supersolutions for a class of doubly nonlinear parabolic fractional p-Laplace equations which includes the fractional parabolic p-Laplace equation and the fractional porous medium equation. More precisely, we show that weak supersolutions have lower semicontinuous representative. We also prove that the semicontinuous representative at an instant of time is determined by the values at previous times. This gives a pointwise interpretation for a weak supersolution at every point. The corresponding results hold true also for weak subsolutions. Our results extend some recent results in the local parabolic case, and in the nonlocal elliptic case, to the nonlocal parabolic case. We prove the required energy estimates and measure theoretic De Giorgi type lemmas in the fractional setting.
Description
Publisher Copyright: © 2022 World Scientific Publishing Company.
Keywords
De Giorgi's method, Doubly nonlinear parabolic equation, energy estimates, fractional p-Laplace equation, porous medium equation
Other note
Citation
Banerjee, A, Garain, P & Kinnunen, J 2023, ' Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic p-Laplace equations ', Communications in Contemporary Mathematics, vol. 25, no. 8, 2250032 . https://doi.org/10.1142/S0219199722500328