In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary‎. ‎We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...

Abstract The main purpose of this paper is to obtain the optimal amount of expenses of government relating to the protection of property rights (PPRs). To achieve these purposes we have introduced concept of social intelligence with respect to PPRs and then developed different growth model from existing literature. In the second step the optimal share of government spending on the PPRs is calcu...