Gradient estimates for elliptic equations with $$L^{p(\cdot )}\log L$$ L p ( · ) log L growth

Ok, Jihoon

doi:10.1007/s00526-016-0965-z

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Cited by 51 publications

(30 citation statements)

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“…have been recently studied, see for instance [7,9,31,55,56,57]. We stress that all of these special cases are covered by the results in this paper (cf.…”

Section: Introductionmentioning

confidence: 77%

Hölder continuity of $\omega$-minimizers of functionals with generalized Orlicz growth

Harjulehto¹,

Hästö²,

Lee³

2021

Annali Scuola Normale Superiore - Classe Di Scienze

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“…have been recently studied, see for instance [7,9,31,55,56,57]. We stress that all of these special cases are covered by the results in this paper (cf.…”

Section: Introductionmentioning

confidence: 77%

Hölder continuity of $\omega$-minimizers of functionals with generalized Orlicz growth

Harjulehto¹,

Hästö²,

Lee³

2021

Annali Scuola Normale Superiore - Classe Di Scienze

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“…that has attracted a lot of attention in the last years [55]; a match between the two cases has been recently proposed in [14,18,24,52,55,56,57]. The growth conditions in (1.5) .7) is non-uniformly elliptic.…”

Section: Introductionmentioning

confidence: 99%

Manifold Constrained Non-uniformly Elliptic Problems

Filippis

Mingione

2019

J Geom Anal

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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 energy features a nonuniformly elliptic integrand exhibiting different polynomial growth conditions and no homogeneity. We develop a few intrinsic methods aimed at proving partial regularity of minima and providing techniques for treating larger classes of similar constrained non-uniformly elliptic variational problems. In order to give estimates for the singular sets we use a general family of Hausdorff type measures following the local geometry of the integrand. A suitable comparison is provided with respect to the naturally associated capacities.

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“…Regarding regularity theory of differential equations, Giannetti and Passarelli di Napoli [12] and Ok [28] as well as Baroni, Colombo and Mingione [2,3,[6][7][8] studied the minimization problems min u  |∇u| p(x) log(e + |∇u|) dx and min…”

Section: Introductionmentioning

confidence: 99%