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001440072 001__ 1440072
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001440072 019__ $$a1273077228$$a1273121547$$a1273977672$$a1287763987
001440072 020__ $$a9783030762599$$q(electronic bk.)
001440072 020__ $$a3030762599$$q(electronic bk.)
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001440072 020__ $$z9783030762582
001440072 0247_ $$a10.1007/978-3-030-76259-9$$2doi
001440072 035__ $$aSP(OCoLC)1272956055
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001440072 049__ $$aISEA
001440072 050_4 $$aQA379
001440072 08204 $$a515/.35$$223
001440072 1001_ $$aDalla Riva, Matteo.
001440072 24510 $$aSingularly perturbed boundary value problems :$$ba functional analytic approach /$$cMatteo Dalla Riva, Massimo Lanza de Cristoforis, Paolo Musolino.
001440072 260__ $$aCham, Switzerland :$$bSpringer,$$c2021.
001440072 300__ $$a1 online resource
001440072 336__ $$atext$$btxt$$2rdacontent
001440072 337__ $$acomputer$$bc$$2rdamedia
001440072 338__ $$aonline resource$$bcr$$2rdacarrier
001440072 347__ $$atext file
001440072 347__ $$bPDF
001440072 504__ $$aIncludes bibliographical references and index.
001440072 5050_ $$a1. Introduction -- 2. Preliminaries -- 3. Preliminaries on Harmonic Functions -- 4. Green Identities and Layer Potentials -- 5. Preliminaries on the Fredholm Alternative Principle -- 6. Boundary Value Problems and Boundary Integral Operators -- 7. Poisson Equation and Volume Potentials -- 8. A Dirichlet Problem in a Domain with a Small Hole -- 9. Other Problems with Linear Boundary Conditions in a Domain with a Small Hole -- 10. A Dirichlet Problem in a Domain with Two Small Holes -- 11. Nonlinear Boundary Value Problems in Domains with a Small Hole -- 12. Boundary Value Problems in Periodic Domains, A Potential Theoretic Approach -- 13. Singular Perturbation Problems in Periodic Domains -- Appendix -- References -- Index.
001440072 506__ $$aAccess limited to authorized users.
001440072 520__ $$aThis book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains. The main purpose is to illustrate a method called Functional Analytic Approach, to describe the dependence of the solutions upon a singular perturbation parameter in terms of analytic functions. Here the focus is on domains with small holes and the perturbation parameter is the size of the holes. The book is the first introduction to the topic and covers the theoretical material and its applications to a series of problems that range from simple illustrative examples to more involved research results. The Functional Analytic Approach makes constant use of the integral representation method for the solutions of boundary value problems, of Potential Theory, of the Theory of Analytic Functions both in finite and infinite dimension, and of Nonlinear Functional Analysis. Designed to serve various purposes and readerships, the extensive introductory part spanning Chapters 17 can be used as a reference textbook for graduate courses on classical Potential Theory and its applications to boundary value problems. The early chapters also contain results that are rarely presented in the literature and may also, therefore, attract the interest of more expert readers. The exposition moves on to introduce the Functional Analytic Approach. A reader looking for a quick introduction to the method can find simple illustrative examples specifically designed for this purpose. More expert readers will find a comprehensive presentation of the Functional Analytic Approach, which allows a comparison between the approach of the book and the more classical expansion methods of Asymptotic Analysis and offers insights on the specific features of the approach and its applications to linear and nonlinear boundary value problems.
001440072 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed October 14, 2021).
001440072 650_0 $$aBoundary value problems.
001440072 650_6 $$aProblèmes aux limites.
001440072 655_7 $$aLlibres electrònics.$$2thub
001440072 655_0 $$aElectronic books.
001440072 7001_ $$aLanza de Cristoforis, Massimo,$$eauthor.
001440072 7001_ $$aMusolino, Paolo,$$eauthor.
001440072 77608 $$iPrint version:$$aDalla Riva, Matteo.$$tSingularly perturbed boundary value problems.$$dCham, Switzerland : Springer, 2021$$z3030762580$$z9783030762582$$w(OCoLC)1246352649
001440072 852__ $$bebk
001440072 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-76259-9$$zOnline Access$$91397441.1
001440072 909CO $$ooai:library.usi.edu:1440072$$pGLOBAL_SET
001440072 980__ $$aBIB
001440072 980__ $$aEBOOK
001440072 982__ $$aEbook
001440072 983__ $$aOnline
001440072 994__ $$a92$$bISE