A1 Refereed original research article in a scientific journal
Generalized Orlicz spaces and related PDE
Authors: Harjulehto P, Hasto P, Klen R
Publisher: PERGAMON-ELSEVIER SCIENCE LTD
Publication year: 2016
Journal: Nonlinear Analysis: Theory, Methods and Applications
Journal name in source: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Journal acronym: NONLINEAR ANAL-THEOR
Volume: 143
First page : 155
Last page: 173
ISSN: 0362-546X
DOI: https://doi.org/10.1016/j.na.2016.05.002
Abstract
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.
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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