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Singularly perturbed boundary value ...

Dalla Riva, Matteo.

Singularly perturbed boundary value problemsa functional analytic approach /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Singularly perturbed boundary value problemsby Matteo Dalla Riva, Massimo Lanza de Cristoforis, Paolo Musolino.
其他題名:	a functional analytic approach /
作者:	Dalla Riva, Matteo.
其他作者:	Lanza de Cristoforis, Massimo.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xvi, 672 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Boundary value problems.
電子資源:	https://doi.org/10.1007/978-3-030-76259-9
ISBN:	9783030762599$q(electronic bk.)

Singularly perturbed boundary value problemsa functional analytic approach /
Dalla Riva, Matteo.

Singularly perturbed boundary value problemsa functional analytic approach /[electronic resource] :by Matteo Dalla Riva, Massimo Lanza de Cristoforis, Paolo Musolino. - Cham :Springer International Publishing :2021. - xvi, 672 p. :ill., digital ;24 cm.

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.

ISBN: 9783030762599$q(electronic bk.)

Standard No.: 10.1007/978-3-030-76259-9doiSubjects--Topical Terms:

206979
Boundary value problems.

LC Class. No.: QA379

Dewey Class. No.: 515.35

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520 $a 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.
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