TY - JOUR
T1 - Some local properties of subsolution and supersolutions for a doubly nonlinear nonlocal p-Laplace equation
AU - Banerjee, Agnid
AU - Garain, Prashanta
AU - Kinnunen, Juha
N1 - 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.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - De Giorgi’s method
KW - Doubly nonlinear parabolic equation
KW - Energy estimates
KW - Fractional p-Laplace equation
UR - http://www.scopus.com/inward/record.url?scp=85119082742&partnerID=8YFLogxK
U2 - 10.1007/s10231-021-01177-4
DO - 10.1007/s10231-021-01177-4
M3 - Article
AN - SCOPUS:85119082742
SN - 0373-3114
VL - 201
SP - 1717
EP - 1751
JO - Annali di Matematica Pura ed Applicata
JF - Annali di Matematica Pura ed Applicata
ER -