Potential estimates for solutions of nonstandard growth measure data problems

Speaker(s)

Anna Zatorska-Goldstein

Affiliation

University of Warsaw

Date

Nov. 9, 2020, 3 p.m.

Information about the event

Zoom

Seminar

Monday's Nonstandard Seminar joint with Seminar of Section of Differential Equations

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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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