Regularity for general functionals with double phase

P Baroni, M Colombo, G Mingione - Calculus of Variations and Partial …, 2018‏ - Springer
We prove sharp regularity results for a general class of functionals of the type w ↦ ∫ F (x, w,
Dw)\, dx, w↦∫ F (x, w, D w) dx, featuring non-standard growth conditions and non-uniform …

Gradient regularity in mixed local and nonlocal problems

C De Filippis, G Mingione - Mathematische Annalen, 2024‏ - Springer
Minimizers of functionals of the type w ↦ ∫ Ω [ | D w | p - f w ] d x + ∫ R n ∫ R n | w ( x ) - w (
y ) | γ | x - y | n + s γ d x d y \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} …

Lipschitz bounds and nonautonomous integrals

C De Filippis, G Mingione - Archive for Rational Mechanics and Analysis, 2021‏ - Springer
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-
valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The …

Lipschitz bounds and nonuniform ellipticity

L Beck, G Mingione - Communications on Pure and Applied …, 2020‏ - Wiley Online Library
We consider nonuniformly elliptic variational problems and give optimal conditions
guaranteeing the local Lipschitz regularity of solutions in terms of the regularity of the given …

Nonlocal equations with measure data

T Kuusi, G Mingione, Y Sire - Communications in Mathematical Physics, 2015‏ - Springer
We develop an existence, regularity and potential theory for nonlinear integrodifferential
equations involving measure data. The nonlocal elliptic operators considered are possibly …

[HTML][HTML] Higher Hölder regularity for the fractional p-Laplacian in the superquadratic case

L Brasco, E Lindgren, A Schikorra - Advances in Mathematics, 2018‏ - Elsevier
We prove higher Hölder regularity for solutions of equations involving the fractional p-
Laplacian of order s, when p≥ 2 and 0< s< 1. In particular, we provide an explicit Hölder …

On the regularity of minima of non-autonomous functionals

C De Filippis, G Mingione - The Journal of Geometric Analysis, 2020‏ - Springer
We consider regularity issues for minima of non-autonomous functionals in the Calculus of
Variations exhibiting non-uniform ellipticity features. We provide a few sharp regularity …

Vectorial nonlinear potential theory.

T Kuusi, G Mingione - Journal of the European Mathematical Society …, 2018‏ - ems.press
We settle the longstanding problem of establishing pointwise potential estimates for vectorial
solutions u:→ RN to the non-homogeneous p-Laplacean system− div (| Du| p− 2 Du)= µ in⊂ …

A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces

I Chlebicka - Nonlinear Analysis, 2018‏ - Elsevier
Abstract The Musielak–Orlicz setting unifies variable exponent, Orlicz, weighted Sobolev,
and double-phase spaces. They inherit technical difficulties resulting from general growth …

A borderline case of Calderón–Zygmund estimates for nonuniformly elliptic problems

C De Filippis, G Mingione - St. Petersburg Mathematical Journal, 2020‏ - ams.org
A borderline case of Calderón–Zygmund estimates for nonuniformly elliptic problems Page 1
Algebra i analiz St. Petersburg Math. J. Tom 31 (2019), 3 Vol. 31 (2020), No. 3, Pages 455–477 …