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Titlebook: Singularly Perturbed Boundary Value Problems; A Functional Analyti Matteo Dalla Riva,Massimo Lanza de Cristoforis,Pao Book 2021 Springer Na

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发表于 2025-3-21 19:31:08 | 显示全部楼层 |阅读模式
书目名称Singularly Perturbed Boundary Value Problems
副标题A Functional Analyti
编辑Matteo Dalla Riva,Massimo Lanza de Cristoforis,Pao
视频videohttp://file.papertrans.cn/868/867957/867957.mp4
概述Presents the effect of perturbations in terms of analytic functions instead of in terms of the more classical asymptotic expansions.Shows a powerful tool for the analysis of nonlinear and non-variatio
图书封面Titlebook: Singularly Perturbed Boundary Value Problems; A Functional Analyti Matteo Dalla Riva,Massimo Lanza de Cristoforis,Pao Book 2021 Springer Na
描述.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 a
出版日期Book 2021
关键词boundary value problem; Functional Analytic Approach; perturbation methods; continuum mechanics; Potenti
版次1
doihttps://doi.org/10.1007/978-3-030-76259-9
isbn_softcover978-3-030-76261-2
isbn_ebook978-3-030-76259-9
copyrightSpringer Nature Switzerland AG 2021
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Preliminaries on Harmonic Functions,d in particular to Evans (., volume 19 of .. American Mathematical Society, Providence, RI, second edition, 2010), Folland (.. Princeton University Press, Princeton, NJ, second edition, 1995), and Gilbarg and Trudinger (., volume 224 of .. Springer-Verlag, Berlin, second edition, 1983). We present t
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Preliminaries on the Fredholm Alternative Principle,,1970), on Fredholm operators in dual systems. The present chapter’s purpose is to introduce these results. We also recall some classical theorems of Functional Analysis in Banach spaces. We do not include proofs, however, as these can be found in monographs such as those of Kress (., volume 82 of .
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Poisson Equation and Volume Potentials,nsider the case of weakly singular kernels, and then the case in which the first order partial derivatives of the kernel are also weakly singular. That been done, we turn to singular kernels and, after that, to weakly singular kernels with singular first order partial derivatives. Finally, we prove
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Other Problems with Linear Boundary Conditions in a Domain with a Small Hole,n a bounded domain with a small hole that shrinks to an interior point. In this chapter we are going to see that the same method also works with other boundary value problems with linear boundary conditions, provided that we introduce a suitable integral representations of the solution. Instead, non
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