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

Fumi-Yuki Maeda; Takao Ohno; Tetsu Shimomura

doi:10.2748/tmj/1552100442

Fumi-Yuki Maeda, Takao Ohno, Tetsu Shimomura

著者情報

キーワード: Metric measure space, Newtonian space, Musielak-Orlicz space, Poincaré inequality, Dirichlet energy integral, obstacle problem, superminimizer

ジャーナルフリー

2019 年 71 巻 1 号 p. 53-68

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

詳細

抄録

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.

責任著者(Corresponding author)

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