115 citations · 176 across the 17 of their papers we have counts for
21 papers · 1 filter
Light rays of Lorentzian graphs and the Born-Infeld model
Cristiana De Filippis, Giuseppe Mingione
Following a program outlined by Bartnik, and also employing nonlinear potential techniques we developed in the last years, we study lightlike singularities of variational solutions…
The Singular Set of Minima of Multiple Integrals
Cristiana De Filippis, Jan Kristensen, Giuseppe Mingione +1
The Hausdorff dimension of the singular set of local minimizers of quasiconvex integrals is strictly less than the ambient dimension.
Necessity of Ladyzhenskaya \& Ural'tseva's sufficient conditions in nonuniform ellipticity
Cristiana De Filippis
The sufficient conditions of Ladyzhenskaya \& Ural'tseva \cite{lu70} for interior gradient estimates in nonuniformly elliptic problems are found to be also necessary. Specifically,…
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 $n…
Sketches of Nonuniformly Elliptic Schauder Theory
Cristiana De Filippis
Schauder theory is a basic tool in the study of elliptic and parabolic PDEs, asserting that solutions inherit the regularity of the coefficients. It plays a central role in establi…
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 .
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.
Quantified Legendreness and the regularity of minima
Cristiana De Filippis, Lukas Koch, Jan Kristensen
We introduce a new quantification of nonuniform ellipticity in variational problems via convex duality, and prove higher differentiability and -smoothness results for vector va…
Regularity for double phase problems at nearly linear growth
Cristiana De Filippis, Giuseppe Mingione
Minima of functionals of the type $$ w\mapsto \int_Ω\left[\snr{Dw}\log(1+\snr{Dw})+a(x)\snr{Dw}^{q}\right] \dx\,, \quad 0\leq a(\cdot) \in C^{0, α}\,,$$ with $Ω\subset \er^n$, have…
Borderline global regularity for nonuniformly elliptic systems
Cristiana De Filippis, Mirco Piccinini
We establish sharp global regularity results for solutions to nonhomogeneous, nonunifomrly elliptic systems with zero boundary conditions. In particular, we obtain everywhere Lipsc…
Singular multiple integrals and nonlinear potentials
Cristiana De Filippis, Bianca Stroffolini
We prove sharp partial regularity criteria of nonlinear potential theoretic nature for the Lebesgue-Serrin-Marcellini extension of nonhomogeneous singular multiple integrals featur…
Quasiconvexity and partial regularity via nonlinear potentials
Cristiana De Filippis
We show how to infer sharp partial regularity results for relaxed minimizers of degenerate, nonuniformly elliptic quasiconvex functionals, using tools from Nonlinear Potential Theo…
Lipschitz bounds and nonautonomous integrals
Cristiana De Filippis, Giuseppe Mingione
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The fun…
Regularity results for a class of non-autonomous obstacle problems with -growth
Cristiana De Filippis
We study some regularity issues for solutions of non-autonomous obstacle problems with -growth. Under suitable assumptions, our analysis covers the main models available in…
Manifold constrained non-uniformly elliptic problems
Cristiana De Filippis, Giuseppe Mingione
We consider the problem of minimizing variational integrals defined on \cc{nonlinear} Sobolev spaces of competitors taking values into the sphere. The main novelty is that the unde…
Hölder regularity for nonlocal double phase equations
Cristiana De Filippis, Giampiero Palatucci
We prove some regularity estimates for viscosity solutions to a class of possible degenerate and singular integro-differential equations whose leading operator switches between two…
On the regularity of the -minima of -functionals
Cristiana De Filippis
We focus on some regularity properties of -minima of variational integrals with -growth and we provide an upper bound on the Hausdorff dimension of their singular set.
Regularity for multi-phase variational problems
Cristiana De Filippis, Jehan Oh
We prove regularity for local minimizers of the \oh{multi-phase} energy: \begin{flalign*} w \mapsto \int_Ω\snr{Dw}^{p}+a(x)\snr{Dw}^{q}+b(x)\snr{Dw}^{s} \ dx, \end{flalig…
Higher Integrability for Constrained Minimizers of Integral Functionals with (p,q)-Growth in low dimension
Cristiana De Filippis
We prove higher summability for the gradient of minimizers of strongly convex integral functionals of the Calculus of Variations with (p,q)-Growth conditions in low dimension. Our…