4 papers · 1 filter
Partial regularity in nonlocal systems I
Cristiana De Filippis, Giuseppe Mingione, Simon Nowak
Solutions to nonlinear integro-differential systems are regular outside a negligible closed subset whose Hausdorff dimension can be explicitly bounded from above. This subset can b…
Partial regularity in nonlocal systems II
Cristiana De Filippis, Giuseppe Mingione, Simon Nowak
Solutions to nonlinear nonlocal systems of order in are , for every , outside a closed singular set whose Hausdorff dimension is less than…
Gradient regularity and first-order potential estimates for a class of nonlocal equations
Tuomo Kuusi, Simon Nowak, Yannick Sire
We consider nonlocal equations of order larger than one with measure data and prove gradient regularity in Sobolev and Hölder spaces as well as pointwise bounds of the gradient in…
Nonlinear nonlocal potential theory at the gradient level
Lars Diening, Kyeongbae Kim, Ho-Sik Lee +1
The aim of this work is to establish numerous interrelated gradient estimates in the nonlinear nonlocal setting. First of all, we prove that weak solutions to a class of homogeneou…