Approximate Solutions to the Discontinuous Riemann-Hilbert Problem of Elliptic Systems of First Order Complex Equations

• 作者: Dechang Chen Guochun Wen Yanhui Zhang
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: DISCONTINUOUS RIEMANN-HILBERT Problem ELLIPTIC Systems of First Order Complex Equations Esti-mates and EXISTENCE of Solutions Multiply CONNECTED DOMAINS
• 年，卷（期）: 2014,（10）
• 页码范围: 1546-1556
• 页数: 11页
• 分类号: O1

摘要

Several approximate methods have been used to find approximate solutions of elliptic systems of first order equations. One common method is the Newton imbedding approach, i.e. the parameter extension method. In this article, we discuss approximate solutions to discontinuous Riemann-Hilbert boundary value problems, which have various applications in mechanics and physics. We first formulate the discontinuous Riemann-Hilbert problem for elliptic systems of first order complex equations in multiply connected domains and its modified well-posedness, then use the parameter extensional method to find approximate solutions to the modified boundary value problem for elliptic complex systems of first order equations, and then provide the error estimate of approximate solutions for the discontinuous boundary value problem.