Stability Of Some Boundary Value Problems With Square Roots With Respect To Path Of Boundary

Lu Jianke professor introduce the Riemann boundary value problem with square roots and the Hilbert boundary value problem with square roots in literature [1],and give the solutions of those problems when the index satisfied some conditions. Based on this concept, we discuss the stability of the solutions to some of boundary value problems with square roots when the boundary curve occurs smooth perturbation.Denoting the unit circle by L and denoting the bounded connected region on the complex plan by E and L(?), all those known function satisfied Holder condition on EGenerally, the solutions of some of boundary value problem with square roots have an even number of zeros of odd order. We think that those zeros will also have correspondent perturbation when the curve occurs perturbation, this increases the difficulty of the issues discussed.This paper discussed the stability of the solutions to some boundary value problems with square roots, they are followings:First, the Hilbert boundary value problem with square roots. we give some error estimation between the following two singular integral,Then we use the result to discuss the stability of Hilbert boundary value problem with square roots when the index satisfied some conditions and give correspondent error estimation.Second, the Riemann boundary value problem with square roots. At first, we give some error estimation between the following two singular integral.Then we use the result to discuss the stability of Riemann boundary value problem with square roots when the index satisfied some conditions and give correspondent error estimation.Third, we give the formula of the solution of the invert Riemann boundary value problem with square roots under the condition of the index satisfied κ+κ≥m+n, when the curve occurs perturbation. Then we discuss the stability of the solution of the invert Riemann boundary value with square roots and its correspondent errorestimation.