Tohoku Mathematical Journal
2021
March
SECOND SERIES VOL. 73, NO. 1

Tohoku Math. J.
73 (2021), 119-136

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

Author Toshihide Futamura and Tetsu Shimomura

(Received August 19, 2019, revised January 17, 2020)
Abstract. We prove the existence and uniqueness of a solution to a double obstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaces supporting a $\Phi$-Poincaré inequality, as an extension of [9, 26]. We also study continuous dependence on obstacles for the double obstacle problem in our setting.

Mathematics Subject Classification. Primary 46E35; Secondary 31B15.
Key words and phrases. Metric measure space, Newtonian space, Musielak-Orlicz space, Poincaré inequality, Dirichlet energy integral, double obstacle problem.

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