Local boundedness of variational solutions to nonlocal double phase parabolic equations

We prove local boundedness of variational solutions to the double phase equation∂tu+P.V.∫RN|u(x,t)−u(y,t)|p−2(u(x,t)−u(y,t))|x−y|N+ps+a(x,y)|u(x,t)−u(y,t)|q−2(u(x,t)−u(y,t))|x−y|N+qs′dy=0, under the restrictions s,s′∈(0,1),1

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Bibliographic Details
Published in:Journal of Differential Equations 2023-04, Vol.351, p.243-276
Main Authors: Prasad, Harsh, Tewary, Vivek
Format: Article
Language:English
Subjects:
Boundedness
Nonlocal operators with nonstandard growth
Parabolic minimizers
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Summary:We prove local boundedness of variational solutions to the double phase equation∂tu+P.V.∫RN|u(x,t)−u(y,t)|p−2(u(x,t)−u(y,t))|x−y|N+ps+a(x,y)|u(x,t)−u(y,t)|q−2(u(x,t)−u(y,t))|x−y|N+qs′dy=0, under the restrictions s,s′∈(0,1),1
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2022.12.029