Cauchy problem for Laplace equation: An observer based approach

A method to solve Cauchy Problem for Laplace equation using state observers is proposed. It is known that this problem is ill-posed. The domain under consideration is simple lipschitz in ℝ
²
with a hole. The idea is to recover the solution over whole domain from the observations on outer boundary. Proposed approach adapts one of the space variables as a time variable. The observer developed to solve Cauchy problem for the Laplace's equation is compuationally robust and accurate.