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

@article{Harjulehto2019HlderCO, title={H{\"o}lder continuity of \$\omega\$-minimizers of functionals with generalized Orlicz growth}, author={Petteri Harjulehto and Peter A. Hasto and Mikyoung Lee}, journal={ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE}, year={2019} }

We show local Holder continuity of quasiminimizers of functionals with non-standard (Musielak--Orlicz) growth. Compared with previous results, we cover more general minimizing functionals and need fewer assumptions. We prove Harnack's inequality and a Morrey type estimate for quasiminimizers. Combining this with Ekeland's variational principle, we obtain local Holder continuity for $\omega$-minimizers.

## 17 Citations

### Hölder Continuity of the Minimizer of an Obstacle Problem with Generalized Orlicz Growth

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We prove local $C^{0,\alpha }$- and $C^{1,\alpha }$-regularity for the local solution to an obstacle problem with nonstandard growth. These results cover as special cases standard, variable…

### Harnack Inequality for Quasilinear Elliptic Equations in Generalized Orlicz-Sobolev Spaces

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In this paper we prove, by a new method, the Harnack inequality for positive solutions of quasilinear elliptic equations in the generalized Orlicz-Sobolev space setting. Our approach is based on the…

### Global gradient estimates for a general class of quasilinear elliptic equations with Orlicz growth

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We provide an optimal global Calderón-Zygmund theory for quasilinear elliptic equations of a very general form with Orlicz growth on bounded nonsmooth domains under minimal regularity assumptions of…

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### Generalized Superharmonic Functions with Strongly Nonlinear Operator

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- 2020

We study properties of $\mathcal{A}$-harmonic and $\mathcal{A}$-superharmonic functions involving an operator having generalized Orlicz-growth embracing besides Orlicz case also natural ranges of…

### Continuity at a boundary point of solutions to quasilinear elliptic equations with generalized Orlicz growth and non-logarithmic conditions

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Abstract We consider the Dirichlet problem for quasilinear elliptic equations with Musielak-Orlicz (p, q)-growth and non-logarithmic conditions on the coefficients. A sufficient Wiener-type condition…

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<abstract><p>We prove sharp reverse Hölder inequalities for minima of multi-phase variational integrals and apply them to Calderón-Zygmund estimates for nonhomogeneous problems.</p></abstract>

### Removable sets in non-uniformly elliptic problems

- MathematicsAnnali di Matematica Pura ed Applicata (1923 -)
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Fine properties of solutions to quasilinear elliptic equations with double-phase structure are analyzed and the size of the removable sets for Hölder continuous solutions is characterized in the terms of intrinsic Hausdorff measures.

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We study the elliptic inclusion given in the following divergence form $$\begin{aligned}&-\mathrm {div}\,A(x,\nabla u) \ni f\quad \mathrm {in}\quad \Omega ,\\&u=0\quad \mathrm {on}\quad \partial…

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