5 papers
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…
Coarse-grained ellipticity and De Giorgi-Nash-Moser theory
Scott Armstrong, Benny Avelin, Cristiana De Filippis +2
We prove local boundedness and a Harnack inequality for nonnegative weak solutions of the equation under a coarse-grained ellipticity assump…
Nonuniform ellipticity in variational problems and regularity
Cristiana De Filippis, Giuseppe Mingione
We provide a brief outlook on recent developments in regularity theory for nonuniformly elliptic problems, with special emphasis on those of variational nature.
The sharp growth rate in nonuniformly elliptic Schauder theory
Cristiana De Filippis, Giuseppe Mingione
Schauder estimates hold in nonuniformly elliptic problems under optimal assumptions on the growth of the ellipticity ratio.