The Gehring Lemma: Dimension free estimates

Kristensen, Jan; Stroffolini, Bianca

doi:10.1016/j.na.2018.06.017

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Uniform Ellipticity and Proof Of Theorem 421

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2021

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“…Given the inequalities in (10.6)-(10.7), and the representation in (10.4)-(10.5), we can proceed for instance as in [29,Lemma 5] to get a global gradient integrability result; this also involves estimates as in (10.2) to treat the additional f -terms appearing here with respect to the case considered in [29]. This involves a matching of local and up-to-the-boundary versions of Gehring's lemma (see [49]). parameters this means that c * depends only on n, N , ν 0 , Λ, γ, a.…”

Section: Uniform Ellipticity and Proof Of Theorem 42mentioning

confidence: 99%

Lipschitz Bounds and Nonautonomous Integrals

Filippis

Mingione

2021

Arch Rational Mech Anal

106

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We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions to those with fast, exponential type growth. The results obtained are sharp with respect to all the data considered and also yield new, optimal regularity criteria in the classical uniformly elliptic case. We give a classification of different types of nonuniform ellipticity, accordingly identifying suitable conditions to get regularity theorems.

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Section: Uniform Ellipticity and Proof Of Theorem 42mentioning

confidence: 99%