HP estimation for the Cauchy problem for nonlinear elliptic equation

Abstract

In this paper, we investigate the Cauchy problem for a ND nonlinear elliptic equation in a bounded domain. As we know, the problem is severely ill-posed. We apply the Fourier truncation method to regularize the problem. Error estimates between the regularized solution and the exact solution are established in H^p space under some priori assumptions on the exact solution.