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.


Dirichlet energy integral, Existence of solution, Musielak-Orlicz spaces, Nonstandard growth, Orlicz space, Poincare inequality, Sobolev space, Variable exponent



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