Recent developments in problems with nonstandard growth and nonuniform ellipticity

G Mingione, V Rădulescu - Journal of Mathematical Analysis and …, 2021 - Elsevier
Recent developments in problems with nonstandard growth and nonuniform ellipticity -
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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 …

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 …

Local Lipschitz continuity for p, q− PDEs with explicit u− dependence

P Marcellini - Nonlinear Analysis, 2023 - Elsevier
This article is dedicated to Emmanuele Di Benedetto, great mathematician, colleague,
friend. In the spirit to treat a subject that in the last years attracted the interest of several …

Maximal regularity for local minimizers of non-autonomous functionals

P Hästö, J Ok - Journal of the European Mathematical Society, 2021 - ems.press
Maximal regularity for local minimizers of non-autonomous functionals Page 1 © 2021
European Mathematical Society Published by EMS Press. This work is licensed under a CC BY …

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 …

Nonuniformly elliptic Schauder theory

C De Filippis, G Mingione - Inventiones mathematicae, 2023 - Springer
Nonuniformly elliptic Schauder theory | Inventiones mathematicae Skip to main content
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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 …

Manifold constrained non-uniformly elliptic problems

C De Filippis, G Mingione - The Journal of Geometric Analysis, 2020 - Springer
We consider the problem of minimizing variational integrals defined on nonlinear Sobolev
spaces of competitors taking values into the sphere. The main novelty is that the underlying …