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A mollification regularization method for the Cauchy problem of an elliptic equation in a multi-dimensional case. (English) Zbl 1206.65224

A Cauchy problem for an elliptic equation is considered. This problem is ill-posed since the solution, if it exists, does not depend continuously on the data. The considered ill-posed problem is replaced by a problem with mollified data and some error estimates between the solutions of the two problems are established. Moreover, some numerical experiments are presented to verify the proposed regularization method.

MSC:

65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
35R25 Ill-posed problems for PDEs
35J25 Boundary value problems for second-order elliptic equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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