Local Lipschitz continuity for energy integrals with slow growth

We pursue the study of a model convex functional with orthotropic structure and nonstandard growth conditions, this time focusing on the sub-quadratic case. We prove that bounded local minimizers are locally Lipschitz. No restriction on the ratio between the highest and the lowest growth rates are needed. The result holds also in presence of a non-autonomous lower order term, under sharp integrability assumptions. Finally, we prove higher differentiability of bounded local minimizers, as well.

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“…Even worse, in contrast with the general framework of [28], in our situation there is no continuous functions…”

Section: 3mentioning

confidence: 80%

“…In [28,Corollary 3.4], the authors proves the local Lipschitz continuity of local minimizers (not a priori bounded) of the following functional…”

Section: 3mentioning

confidence: 99%

Lipschitz regularity for orthotropic functionals with nonstandard growth conditions

Bousquet

Brasco

2020

Rev. Mat. Iberoam.

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“…of the material has been published on-line in August-September 2021 and it can be found in the papers [7,8].…”

Section: Lectures Of the Conferencementioning

confidence: 99%

Advances in Singular and Degenerate PDEs

Fragapane

2022

Mathematics

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This review was written with a dual purpose; on the one hand, to collect all the topics dealt with during the conference “Advances in Singular and Degenerate PDEs”. For this reason, in the first part of this work, the abstracts of the lectures during the workshop are shown. On the other hand, as well as the workshop, this work is a way to celebrate the career of Professor Maria Agostina Vivaldi. Professor Vivaldi’s long career and her work are hence highlighted in this work; moreover, some of the more recent results obtained by Professor Vivaldi about problems involving p-Laplace-type operators in fractal and pre-fractal boundary domains are here illustrated and discussed. In conclusion, some new recent outcomes and new perspectives are outlined.

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“…Functionals with nearly linear growth have been the object of intensive investigation over the years. For this we mention, for instance, [22,23,24,101,109,111,178]. Their nonuniform ellipticity stems from their closeness to linear growth functionals, like for instance the minimal surface one, that are always nonuniformly elliptic; for this see [15,16,123,122,124,125] and related references for recent developments.…”

Section: Schauder Estimates At Nearly Linear Growth [81]mentioning

confidence: 99%

Nonuniformly elliptic problems

Mingione

2021

Preprint

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Regularity for nonuniformly elliptic problems has been developed intensively over the last years, especially due to the interest raised by a few special model examples coming from the Calculus of Variations. I shall first give a brief overview of main results in the variational setting and then I shall present some more recent ones obtained in collaboration with Cristiana De Filippis (Università di Torino).

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Local Lipschitz continuity for energy integrals with slow growth

Cited by 13 publications

References 42 publications

Lipschitz regularity for orthotropic functionals with nonstandard growth conditions

Lipschitz regularity for orthotropic functionals with nonstandard growth conditions

Advances in Singular and Degenerate PDEs

Nonuniformly elliptic problems

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