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Regularity for general functionals with double phase
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 …
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
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} …
y ) | γ | x - y | n + s γ d x d y \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} …
Lipschitz bounds and nonautonomous integrals
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-
valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The …
valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The …
Lipschitz bounds and nonuniform ellipticity
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 …
guaranteeing the local Lipschitz regularity of solutions in terms of the regularity of the given …
Nonlocal equations with measure data
We develop an existence, regularity and potential theory for nonlinear integrodifferential
equations involving measure data. The nonlocal elliptic operators considered are possibly …
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
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 …
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
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 …
Variations exhibiting non-uniform ellipticity features. We provide a few sharp regularity …
Vectorial nonlinear potential theory.
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⊂ …
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
Abstract The Musielak–Orlicz setting unifies variable exponent, Orlicz, weighted Sobolev,
and double-phase spaces. They inherit technical difficulties resulting from general growth …
and double-phase spaces. They inherit technical difficulties resulting from general growth …
A borderline case of Calderón–Zygmund estimates for nonuniformly elliptic problems
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 …
Algebra i analiz St. Petersburg Math. J. Tom 31 (2019), 3 Vol. 31 (2020), No. 3, Pages 455–477 …