Potential estimates for solutions of nonstandard growth measure data problems

Prelegent(ci)

Anna Zatorska-Goldstein

Afiliacja

University of Warsaw

Termin

9 listopada 2020 15:00

Informacje na temat wydarzenia

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Seminarium

Poniedziałkowe Niestandardowe Seminarium łączone z Seminarium Zakładu Równań Różniczkowych

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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.

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