9 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…
Bounded minimizers of double phase problems at nearly linear growth
Cristiana De Filippis, Filomena De Filippis, Mirco Piccinini
Bounded minimizers of double phase problems at nearly linear growth have locally Hölder continuous gradient within the sharp maximal nonuniformity range .
Intrinsic Schauder estimates at nearly linear growth
Cristiana De Filippis, Filomena De Filippis, Peter Hästö
We develop a nonlinear potential theoretic framework for Schauder estimates for vector-valued solutions of a broad class of nonautonomous variational problems at nearly linear grow…
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…
-ellipticity and nonautonomous integrals
Cristiana De Filippis
-ellipticity is a form of nonuniform ellipticity arising in various contexts from the calculus of variations. Understanding regularity properties of minimizers in the nonautono…