Abstract
We prove local boundedness and Hölder continuity for weak solutions to nonlocal double phase problems concerning the following fractional energy functional∫Rn∫Rn|v(x)−v(y)|p|x−y|n+sp+a(x,y)|v(x)−v(y)|q|x−y|n+tqdxdy, where 0<s≤t<1<p≤q<∞ and a(⋅,⋅)≥0. For such regularity results, we identify sharp assumptions on the modulating coefficient a(⋅,⋅) and the powers s,t,p,q which are analogous to those for local double phase problems.
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