Hölder regularity for weak solutions to nonlocal double phase problems

By Sun-Sig Byun, Jihoon Ok, Kyeong Song. Journal des Mathématiques Pures et Appliquées, 2021

64 citations recorded by the source corpus.

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)| |x− y|n+sp + a(x, y) |v(x) − v(y)| |x− y|n+tq dxdy, 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/63cedaf4fcca55c2703f31f9100240bbfaf5caa9

Citations in the corpus

• Local Hölder continuity for fractional nonlocal equations with general growth (2021, unknown): “Recently there has been a great deal of studies concerning fractional nonlocal equations with nonstandard growth conditions, in particular for Hölder regularity in [7, 45] with the variable growth condition and in [4, 12, 20] with the double phase condition, respectively.”