東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Singularly perturbed boundary value ...

Dalla Riva, Matteo.

Linked to FindBook

Google Book

Amazon

博客來

Singularly perturbed boundary value problems = a functional analytic approach /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Singularly perturbed boundary value problems/ by Matteo Dalla Riva, Massimo Lanza de Cristoforis, Paolo Musolino.
Reminder of title:	a functional analytic approach /
Author:	Dalla Riva, Matteo.
other author:	Lanza de Cristoforis, Massimo.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	xvi, 672 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Boundary value problems. -
Online resource:	https://doi.org/10.1007/978-3-030-76259-9
ISBN:	9783030762599

Singularly perturbed boundary value problems = a 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

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

527599
Boundary value problems.

LC Class. No.: QA379

Dewey Class. No.: 515.35

Singularly perturbed boundary value problems = a functional analytic approach /
LDR:03634nmm a2200325 a 4500 001 2251484
003 DE-He213
005 20211001002814.0
006 m d
007 cr nn 008maaau
008 220215s2021 sz s 0 eng d
020 $a 9783030762599 $q (electronic bk.)
020 $a 9783030762582 $q (paper)
024 7 $a 10.1007/978-3-030-76259-9 $2 doi
035 $a 978-3-030-76259-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QA379
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.35 $2 23
090 $a QA379 $b .D144 2021
100 1 $a Dalla Riva, Matteo. $3 3518537
245 1 0 $a Singularly perturbed boundary value problems $h [electronic resource] : $b a functional analytic approach / $c by Matteo Dalla Riva, Massimo Lanza de Cristoforis, Paolo Musolino.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xvi, 672 p. : $b ill., digital ; $c 24 cm.
505 0 $a 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.
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.
650 0 $a Boundary value problems. $3 527599
650 1 4 $a Partial Differential Equations. $3 890899
650 2 4 $a Ordinary Differential Equations. $3 891264
650 2 4 $a Operator Theory. $3 897311
700 1 $a Lanza de Cristoforis, Massimo. $3 3518538
700 1 $a Musolino, Paolo. $3 3518539
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-030-76259-9
950 $a Mathematics and Statistics (SpringerNature-11649)