Essentially fully anisotropic Orlicz functions and uniqueness to measure data problem. (25th February 2021)

• Record Type: Journal Article
• Authors: Chlebicka, Iwona; Nayar, Piotr
• Other Names: Alaoui Mohammed Kbiri guestEditor.; Messaoudi Salim guestEditor.; Hästö Peter guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 14(2022)
• Page Start: 8503
• Page End: 8527
• Publication Date: 2021-02-25
• Subjects: anisotropy -- capacity -- Lebesgue points -- measures -- Orlicz–Sobolev spaces; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7278
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Studying elliptic measure data problem with strongly nonlinear operator whose growth is described by the means of fully anisotropic N ‐function, we prove the uniqueness for a broad class of measures. In order to provide it, the framework of capacities in fully anisotropic Orlicz–Sobolev spaces is developed and the capacitary characterization of a bounded measure is given. Moreover, we give an example of an anisotropic Young function Φ, such that | ξ | p ≲ Φ ( ξ ) ≲ | ξ | p log α ( 1 + | ξ | ), with arbitrary p ≥ 1, α > 0, but so irregularly growing that the Orlicz–Sobolev‐type space generated by Φ indispensably requires fully anisotropic tools to be handled.