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

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2022
Major/Subject
Mcode
Degree programme
Language
en
Pages
Series
Annali di Matematica Pura ed Applicata
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.
Description
Funding Information: A.B. is supported in part by SERB Matrix grant MTR/2018/000267 and by Department of Atomic Energy, Government of India, under project no. 12-R & D-TFR-5.01-0520. P.G. and J.K. are supported by the Academy of Finland. Publisher Copyright: © 2021, Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature.
Keywords
De Giorgi’s method, Doubly nonlinear parabolic equation, Energy estimates, Fractional p-Laplace equation
Other note
Citation
Banerjee, A, Garain, P & Kinnunen, J 2022, ' Some local properties of subsolution and supersolutions for a doubly nonlinear nonlocal p-Laplace equation ', Annali di Matematica Pura ed Applicata, vol. 201, pp. 1717–1751 . https://doi.org/10.1007/s10231-021-01177-4