The double obstacle problem for Musielak-Orlicz Dirichlet energy integral on metric measure spaces

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.