Potential estimates for solutions of nonstandard growth measure data problems

We study the problem−divA(x,Du) =μ in Ω⊂Rn with a nonnegative bounded measure μ and a Caratheodory function A: Ω×Rn→Rn with Orlicz growth with respect to the second variable. The assumptions naturally cover the case of Laplacian and p-Laplacian. Solutions to such problem can be unbounded, but we can control them by a certain potential of Wolff-type.The estimates we provide have many sharp regularity consequences such as Holder continuity when measure satisfies a density condition in the relevant Orlicz-Morrey scale. Based on joint project with Iwona Chlebicka and Flavia Giannetti; see preprint Wolff potentials and local behaviour of solutions to measure data elliptic problems with Orlicz growth, arXiv:2006.02172.