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＜電子ブック＞
Singularly Perturbed Boundary Value Problems : A Functional Analytic Approach / by Matteo Dalla Riva, Massimo Lanza de Cristoforis, Paolo Musolino

版	1st ed. 2021.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2021
本文言語	英語
大きさ	XVI, 672 p. 4 illus : online resource
著者標目	*Dalla Riva, Matteo author Lanza de Cristoforis, Massimo author Musolino, Paolo author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Operator theory FREE:Analysis FREE:Analysis FREE:Operator Theory
一般注記	1. Introduction -- 2. Preliminaries -- 3. Preliminaries on Harmonic Functions -- 4. Green Identities and Layer Potentials -- 5. Preliminaries on the Fredholm Alternative Principle -- 6. Boundary Value Problems and Boundary Integral Operators -- 7. Poisson Equation and Volume Potentials -- 8. A Dirichlet Problem in a Domain with a Small Hole -- 9. Other Problems with Linear Boundary Conditions in a Domain with a Small Hole -- 10. A Dirichlet Problem in a Domain with Two Small Holes -- 11. Nonlinear Boundary Value Problems in Domains with a Small Hole -- 12. Boundary Value Problems in Periodic Domains, A Potential Theoretic Approach -- 13. Singular Perturbation Problems in Periodic Domains -- Appendix -- References -- Index This book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains. The main purpose is to illustrate a method called Functional Analytic Approach, to describe the dependence of the solutions upon a singular perturbation parameter in terms of analytic functions. Here the focus is on domains with small holes and the perturbation parameter is the size of the holes. The book is the first introduction to the topic and covers the theoretical material and its applications to a series of problems that range from simple illustrative examples to more involved research results. The Functional Analytic Approach makes constant use of the integral representation method for the solutions of boundary value problems, of Potential Theory, of the Theory of Analytic Functions both in finite and infinite dimension, and of Nonlinear Functional Analysis. Designed to serve various purposes and readerships, the extensive introductory part spanning Chapters 1–7 can be used as a reference textbook for graduate courses on classical Potential Theory and its applications to boundary value problems. The early chapters also contain results that are rarely presented in the literature and may also, therefore, attract the interest of more expert readers. The exposition moves on to introduce the Functional Analytic Approach. A reader looking for a quick introduction to the method can find simple illustrative examples specifically designed for this purpose. More expert readers will find a comprehensive presentation of the Functional Analytic Approach, which allows a comparison between the approach of the book and the more classical expansion methods of Asymptotic Analysis and offers insights on the specific features of the approach and its applications to linear and nonlinear boundary value problems HTTP:URL=https://doi.org/10.1007/978-3-030-76259-9

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