Abstract
This chapter discusses analytic methods for the approximate solution of elliptic free boundary value problems (BVPs). It discusses the application of perturbation and iteration methods to certain BVPs for the elliptic partial differential equations of the form Δu + f(x,u) = 0, where x = (x1,…., xn) is a point in Rn, Δ denotes the Laplacian operator, u is a real scalar variable, and f is a piecewise-continuous function of x1,…., xn and u. When f has jump discontinuities with respect to u, among the interfaces across which f changes abruptly, there may be free boundaries that are not known a priori but must be found along with the solution u = u(x).
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