An Inverse Problem for a Nonlinear Elliptic Differential Equation

Abstract

In this paper we determine the form of an unknown forcing term f in the equation $\Delta u = \gamma (x,y,u) + f(u)$ from overprescribed boundary data on a domain in $R^2 $ by reformulating the problem as a fixed point problem in an appropriate function space. Given suitable restrictions on the growth of f and the boundary data we recover a unique f.