Abstract
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<p≤q≤p2s+NN and the non-negative function (x,y)↦a(x,y) is assumed to be measurable and bounded.
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