Regularized solution of a Cauchy problem for stochastic elliptic equation

Abstract

In this study, we investigate a Cauchy problem for the stochastic elliptic equation driven by Wiener noise. We show this problem is not well‐posed by proposing a simple illustrative example. To regularize the instable solution, we apply a regularization method called Fourier truncated expansion method. Furthermore, the convergence rate of the regularized solution is also investigated.