圆环域上Cauchy问题解的条件稳定性估计

A Conditional Stability Estimate for a Cauchy Problem on a Ring Domain

通过引进适当的能量泛函,建立了一个对圆环域上的解依赖于区域大小的Hlder条件稳定性,得到了在局部区域上Hlder型的稳定性估计,为利用条件稳定性确定Tikhonov正则化参数的某些新方法提供了理论基础.

The local conditional stability with respect to the Cauchy input data on a ring domain is established by introducing proper energy functional.We obtain,the Hlder exponent in the estimate depends on the size of the local domain concernedi.This result provides the theoretical foundation for some new scheme of determining the regularizing parameter.