Abstract
We study the double obstacle problem on a metric measure space equipped with a doubling measure and supporting a p-Poincaré inequality. We prove existence and uniqueness. We also prove the continuity of the solution of the double obstacle problem with continuous obstacles and show that the continuous solution is a minimizer in the open set where it does not touch the two obstacles. Moreover we consider the regular boundary points and show that the solution of the double obstacle problem on a regular open set with continuous obstacles is continuous up to the boundary. Regularity of boundary points is further characterized in some other ways using the solution of the double obstacle problem.