Description 
1 online resource 
Contents 
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 
Summary 
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 17 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 
Bibliography 
Includes bibliographical references and index 
Notes 
Online resource; title from PDF title page (SpringerLink, viewed October 14, 2021) 
Subject 
Boundary value problems.


Boundary value problems.


Problemes de contorn.

Genre/Form 
Electronic books


Llibres electrĂ˛nics.

Form 
Electronic book

Author 
Lanza de Cristoforis, Massimo, author


Musolino, Paolo, author

ISBN 
9783030762599 

3030762599 
