Generalized Orlicz spaces and related PDE



: Harjulehto P, Hasto P, Klen R

Publisher: PERGAMON-ELSEVIER SCIENCE LTD

: 2016

: Nonlinear Analysis: Theory, Methods and Applications

: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

: NONLINEAR ANAL-THEOR

: 143

: 155

: 173

: 0362-546X

DOI: https://doi.org/10.1016/j.na.2016.05.002


We prove the boundedness of the maximal operator in generalized Orlicz spaces defined on subsets of R-n. The proof is based on an extension result for Phi-functions. We study generalized Sobolev-Orlicz spaces and establish density of smooth functions and the Poincare inequality. As applications we establish the existence of solutions of the phi-Laplace equation with zero and non-zero right-hand side. Further, we systematize assumptions for Phi-functions and prove several basic tools needed for the study of differential equations of generalized Orlicz growth. (C) 2016 Elsevier Ltd. All rights reserved.



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