20 citations · 24 across the 9 of their papers we have counts for
10 papers
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 $n…
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…
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…
Calderón-Zygmund estimates for the fractional -Laplacian
Lars Diening, Simon Nowak
We prove fine higher regularity results of Calderón-Zygmund-type for equations involving nonlocal operators modelled on the fractional -Laplacian with possibly discontinuous coe…
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…
Improved Sobolev regularity for linear nonlocal equations with VMO coefficients
Simon Nowak
This work is concerned with both higher integrability and differentiability for linear nonlocal equations with possibly very irregular coefficients of VMO-type or even coefficients…
Regularity theory for nonlocal equations with VMO coefficients
Simon Nowak
We prove higher regularity for nonlinear nonlocal equations with possibly discontinuous coefficients of VMO-type in fractional Sobolev spaces. While for corresponding local ellipti…
Higher integrability for nonlinear nonlocal equations with irregular kernel
Simon Nowak
We prove a higher regularity result for weak solutions to nonlinear nonlocal equations along the integrability scale of Bessel potential spaces under a mild continuity as…
Higher Hölder regularity for nonlocal equations with irregular kernel
Simon Nowak
We study the higher Hölder regularity of local weak solutions to a class of nonlinear nonlocal elliptic equations with kernels that satisfy a mild continuity assumption. An interes…
regularity theory for a class of nonlocal elliptic equations
Simon Nowak
In this paper, we study the regularity of weak solutions to a class of nonlocal elliptic equations in Bessel potential spaces . Our main results can be seen as an extensio…