Nonlinear Boundary Value Problems for Holomorphic Functions and Singular Integral Equations
Nonlinear Boundary Value Problems for Holomorphic Functions and Singular Integral Equations
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全纯函数和奇异积分方程的非线性边值问题
DOI：
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发表时间：
1992
期刊：
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通讯作者：
E. Wegert
中科院分区：
文献类型：
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作者：
E. Wegert
本文涵盖了全纯函数非线性边值问题的各种主题，包括存在唯一性、结果、参数依赖性问题、正则性定理、数值解决这类问题的几种方法，以及非线性奇异积分方程的应用。重点主要放在这个问题的几何方面。对经典极大值原理的适当推广，在边值问题和极值问题之间建立了密切的联系，并为全纯函数的插值和逼近以及ho -优化开辟了一条新的途径。在研究非线性奇异积分方程时，人们的兴趣主要集中在解流形的结构上。分岔现象不仅被发现，而且在奇点理论的框架内被分类。提出了解决所考虑问题的数值方法，并报告了实现这些方法的一些经验。这本书只需要基本的函数理论知识，必要的初步知识在单独的一章中总结。
This work covers various topics in nonlinear boundary value problems for holomorphic functions, including existence and uniqueness, results, questions concerning parameter dependence, regularity theorems, several procedures for numerically solving such problems, and applications to nonlinear singular integral equations. The emphasis is mainly on the geometric aspects of the matter. A key role is played by an appropriate generalization of the classical maximum principle, which establishes intimate connections between boundary value problems and extremal problems and also opens a novel approach to interpolation and approximation with holomorphic functions and to Ho-optimization. In the investigation of nonlinear singular integral equations the interest focuses on the structure of the solution manifold. Bifurcation phenomena are not merely detected, but also classified in the framework of singularity theory. Numerical methods for solving the problems considered are proposed and some experience gained in their realization is reported. The book requires only elementary knowledge of function theory, the necessary preliminaries are summarized in a separate chapter.