Abstract

We consider the problem of determining the temperature \(u(x,y)\) in a body represented by the half-plane \(\mathbb R\times \mathbb R^+\) from measurements performed at interior points of the body. The function \(u(x,y)\) satisfies the nonlinear elliptic equation \[ \Delta u =f(x,y,u(x,y)),\quad x\in\mathbb R,\quad y > 0. \] The problem is ill-posed. Using the method of Fourier transforms and the method of truncation, we prove uniqueness and give a regularization result. An error estimate is also given.