Measure data elliptic problems with generalized Orlicz growth

2020/08/06 by Iwona Chlebicka, Chlebicka, Iwona
Mathematics · #Mathematical and Theoretical Analysis #Advanced Topology and Set Theory #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.2008.02495

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.

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