A New Well-Posed Version of Riemann-Hilbert Problem for Elliptic Complex Equations of First Order in Multiply Connected Domains

作者：Wen Guochun^*

来源：Complex Analysis and Operator Theory, 2015, 9(1): 21-34.

DOI：10.1007/s11785-013-0353-z

• Riemann-Hilbert problems
• A new well-posed-ness
• Uniformly elliptic complex equations
• Multiply connected domains
• A priori estimates and existence of solutions
• Equivalence of two kinds of well-posed-ness

In this article, we first propose the Riemann-Hilbert problem for uniformly elliptic complex equations of first order in multiply connected domains and its new well-posed-ness with continuous solutions. Then we obtain a priori estimates of solutions of the modified Riemann-Hilbert problem, and derive the solvability results of the modified and original Riemann-Hilbert problems. Finally we shall verify the equivalence of two kinds of well-posed-ness for the Riemann-Hilbert boundary value problem.

• 出版日期2015-1
• 单位北京大学