ABSTRACT
The obstacle problem is one kind of free boundary problem. It allows us to model, for example, an elastic membrane covering a solid obstacle. In this case, the objective is to find an equilibrium position of this membrane constrained to be above the obstacle and which tends to minimize its surface and/or its energy. The study of such problems occurs in many applications, for example, fluid mechanics, biomathematics (tumor growth process), or financial mathematics (American or European option pricing).
