Some stability estimates for Cauchy problems for elliptic equations

In this paper we consider Cauchy problems for elliptic equations on a cylinclric domain in M. A series of stability estimates for the Cauchy problems in Sobolev spaces are derived, which turn out to be optimal. From the stability estimates, several regularization methods are proposed for which error estimates are available. The regularization methods can be used for computing numerical approximations which will be demonstrated by the classical Hadamard example.