Properties of obstacle problem and free boundary problem

This paper is a paper which is written based on the contents of [1] and introduction of obstacle problem for nonlinear second-order parabolic operator.In chapter 1, we introduce classical obstacle problem and we deal with existence, uniqueness and C 1,1 regularity of solution of the problem.In chapter 2, we show C 1,1 regularity of solution of Obstacle-type problem.In chapter 3, we prove some elementary properties of free boundary.In chapter 4, We reference [2] to show the continuity of solution of obstacle problem for nonlinear second-order parabolic operator.