Measure data elliptic problems with generalized Orlicz growth
Iwona Chlebicka
2022Proceedings of the Royal Society of Edinburgh Section A Mathematics23 citationsDOIOpen Access PDF
Abstract
We study nonlinear measure data elliptic problems involving the operator of 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 for a class of data being diffuse with respect to a relevant nonstandard capacity. A capacitary characterization of diffuse measures is provided.
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