國立虎尾科技大學 |

Singularly Perturbed Boundary Value Problems = A Functional Analytic Approach /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Singularly Perturbed Boundary Value Problems/ by 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:	Musolino, Paolo.
面頁冊數:	XVI, 672 p. 4 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Operator Theory. -
電子資源:	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. - 1st ed. 2021. - XVI, 672 p. 4 illus.online resource.

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:

672127
Operator Theory.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

Singularly Perturbed Boundary Value Problems = A Functional Analytic Approach /
LDR:04011nam a22003975i 4500 001 1054607
003 DE-He213
005 20211001002814.0
007 cr nn 008mamaa
008 220103s2021 sz | s |||| 0|eng d
020 $a 9783030762599 $9 978-3-030-76259-9
024 7 $a 10.1007/978-3-030-76259-9 $2 doi
035 $a 978-3-030-76259-9
050 4 $a QA370-380
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.353 $2 23
100 1 $a Dalla Riva, Matteo. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1359700
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.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a XVI, 672 p. 4 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 2 4 $a Operator Theory. $3 672127
650 2 4 $a Ordinary Differential Equations. $3 670854
650 1 4 $a Partial Differential Equations. $3 671119
650 0 $a Operator theory. $3 527910
650 0 $a Differential equations. $3 527664
650 0 $a Partial differential equations. $3 1102982
700 1 $a Musolino, Paolo. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1359702
700 1 $a Lanza de Cristoforis, Massimo. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1359701
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030762582
776 0 8 $i Printed edition: $z 9783030762605
776 0 8 $i Printed edition: $z 9783030762612
856 4 0 $u https://doi.org/10.1007/978-3-030-76259-9
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)