Essentially fully anisotropic Orlicz functions and uniqueness to measure data problem

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