OBSTACLE PROBLEM FOR MUSIELAK-ORLICZ DIRICHLET ENERGY INTEGRAL ON METRIC MEASURE SPACES

Fumi-Yuki Maeda; Takao Ohno; Tetsu Shimomura

doi:10.2748/tmj/1552100442

Tohoku Mathematical Journal, Second Series

Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735

OBSTACLE PROBLEM FOR MUSIELAK-ORLICZ DIRICHLET ENERGY INTEGRAL ON METRIC MEASURE SPACES

Fumi-Yuki Maeda, Takao Ohno, Tetsu Shimomura

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Keywords: Metric measure space, Newtonian space, Musielak-Orlicz space, Poincaré inequality, Dirichlet energy integral, obstacle problem, superminimizer

JOURNAL FREE ACCESS

2019 Volume 71 Issue 1 Pages 53-68

DOI https://doi.org/10.2748/tmj/1552100442

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Abstract

We introduce Musielak-Orlicz Newtonian space on a metric measure space. After discussing properties of weak upper gradients of functions in such spaces and Poincaré inequalities for functions with zero boundary values in bounded open subsets, we prove the existence and uniqueness of a solution to an obstacle problem for Musielak-Orlicz Dirichlet energy integral.

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