Generalized Orlicz spaces and related PDE. (September 2016) - Harjulehto, Petteri; Hästö, Peter; Klén, Riku
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 Φ -functions. We study generalized Sobolev–Orlicz spaces and establish density of smooth functions and the Poincaré inequality. As applications we establish the existence of solutions of the φ -Laplace equation with zero and non-zero right-hand side. Further, we systematize assumptions for Φ -functions and prove several basic tools needed for the study of differential equations of generalized Orlicz growth.