Measure data elliptic problems with generalized Orlicz growth
Abstract
We study nonlinear measure data elliptic problems involving the operator exposing generalized Orlicz growth. Our framework embraces reflexive Orlicz spaces, as well as natural variants of variable exponent and double-phase spaces. Approximable and renormalized solutions are proven to exist and coincide for arbitrary measure datum and to be unique when the datum is diffuse with respect to a relevant nonstandard capacity. For justifying that the class of measures is natural, a capacitary characterization of diffuse measures is provided.
Cite
@article{arxiv.2008.02495,
title = {Measure data elliptic problems with generalized Orlicz growth},
author = {Iwona Chlebicka},
journal= {arXiv preprint arXiv:2008.02495},
year = {2020}
}
Comments
the study is related to arXiv:2008.02227 but is conducted in some other setting and other type of solutions is investigated; our inspiration is arXiv:1701.08970 with integrable data which we allow here to be a measure