A shape-measure method for solving free-boundary elliptic systems with boundary control function

This article deals with a computational algorithmic approach for obtaining the optimal solution of a general free boundary problem governed by an elliptic equation with boundary control and functional criterion. After determining the weak solution of the system, the problem is converted into a variational format. Then, by using some aspects of measure theory, the method characterize the nearly optimal pair of domain and its related optimal control function at the same time. This method has many advantages such as strong linearity, automatic existence theorem and the ability of obtaining global solution. Two sets of numerical examples is also given.