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Corpus ID: 219259825

Wolff potentials and local behaviour of solutions to measure data elliptic problems with Orlicz growth

@article{Chlebicka2020WolffPA,
title={Wolff potentials and local behaviour of solutions to measure data elliptic problems with Orlicz growth},
author={I. Chlebicka and F. Giannetti and Anna Zatorska–Goldstein},
journal={arXiv: Analysis of PDEs},
year={2020}
}

We establish pointwise estimates expressed in terms of a nonlinear potential of a generalized Wolff type for $A$-superharmonic functions with nonlinear operator $A:\Omega\times\mathbb{R}^n\to\mathbb{R}^n$ having measurable dependence on the spacial variable and Orlicz growth with respect to the last variable. The result is sharp as the same potential controls bounds from above and from below. Applying it we provide a bunch of precise regularity results including continuity and Holder continuity… CONTINUE READING