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.
Publisher
Cambridge University Press (CUP)
Reference71 articles.
1. Well-posedness of parabolic equations in the non-reflexive and anisotropic Musielak–Orlicz spaces in the class of renormalized solutions;Chlebicka;J. Differ. Equ,2018
2. Some properties of reachable solutions of nonlinear elliptic equations with measure data;Dal Maso;Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4),1998
3. Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients
4. Fully anisotropic elliptic problems with minimally integrable data
5. 30 Chlebicka, I. and Karppinen, A. , Sharp conditions for Hölder continuity of solutions to measure data equations with generalized Orlicz growth. preprint.
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献