Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the correspondi...Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well.展开更多
This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed （elliptic- hyperbolic） complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem an...This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed （elliptic- hyperbolic） complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of HSlder continuity of a singular double integer is very difficult and interesting as in this Section 4 below.展开更多
基金the Natural Science Foundation of Zhejiang Province (Y605149)the National Natural Science Foundation of China (10571156)
文摘Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11021161 and 10928102973 Program of China under Grant No.2011CB80800+2 种基金Chinese Academy of Sciences under Grant No.kjcx-yw-s7project grant of "Center for Research and Applications in Plasma Physics and Pulsed Power Technology,PBCT-Chile-ACT 26"Direcci'on de Programas de Investigaci'on,Universidad de Talca,Chile
文摘This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed （elliptic- hyperbolic） complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of HSlder continuity of a singular double integer is very difficult and interesting as in this Section 4 below.
