H?lder regularity for weak solutions to nonlocal double phase problems

We prove local boundedness and Holder continuity for weak solutions to nonlocal double phase problems concerning the following fractional energy functional integral Rn integral Rn |v(x) - v(y)|p/|x - y|n+sp +a(x, y)|v(x) - v(y)|q/|x- y|n+tq dxdy, where 0 < s <= t < 1 < p <= q < infinity and a(center dot, center dot) >= 0. For such regularity results, we identify sharp assumptions on the modulating coefficient a(center dot, center dot) and the powers s, t, p, q which are analogous to those for local double phase problems. (c) 2022 Elsevier Masson SAS. All rights reserved.

Automated summary

We prove local boundedness and Holder continuity for weak solutions to nonlocal double phase problems. Sharp assumptions on the modulating coefficient and the powers are identified, analogous to those for local double phase problems.