Hilbert边值逆问题关于边界曲线的稳定性

On Stability of Inverse Hilbert Boundary Value Problem with Respect to Path of Boundary

当边界曲线发生微小的光滑扰动时,给出指标大于等于零时Hilbert边值逆问题解的状况.借助共形变换理论给出其中解的表达式,并讨论Hilbert边值逆问题解的稳定性,以及给出相应的误差估计.

Using the knowledge of conformal mapping theorem, we discuss the solvability of inverse Hilbert boundary value problem under the small perturbation of boundary curve. When the index of this problem is non-negative, the repre- sentations of the solutions are obtained. We also show the solutions are stable, and give the corresponding error esti- mates.