A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Generalized Orlicz spaces and related PDE
Tekijät: Harjulehto P, Hasto P, Klen R
Kustantaja: PERGAMON-ELSEVIER SCIENCE LTD
Julkaisuvuosi: 2016
Journal: Nonlinear Analysis: Theory, Methods and Applications
Tietokannassa oleva lehden nimi: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Lehden akronyymi: NONLINEAR ANAL-THEOR
Vuosikerta: 143
Aloitussivu: 155
Lopetussivu: 173
ISSN: 0362-546X
DOI: https://doi.org/10.1016/j.na.2016.05.002
Tiivistelmä
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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