Stability of solutions to Hilbert boundary value problem under perturbation of the boundary curve

作者：Zhang HM; Wang CR^*; Zhu YC

来源：Journal of Mathematical Analysis and Applications, 2003, 284(2): 601-617.

DOI：10.1016/S0022-247X(03)00367-6

• Hilbert boundary value problem
• perturbation
• stability
• conformal transformation

In this paper, the authors discuss the stability of the solutions to Hilbert boundary value problem under perturbation of the unit circle. When the index of this problem is non-negative, by extending Lavrentjev's conformal mapping on a region approximating to a unit disc, we show the solutions are stable under small perturbations. For negative index we give a conception of quasi-solution and discuss its stability correspondingly.

• 出版日期2003-8-15
• 单位福州大学