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Titlebook: Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains; Volume I Vladimir Maz’ya,Serguei Nazarov,Boris A. Pl

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發(fā)表于 2025-3-21 18:44:30 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
期刊全稱Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains
期刊簡(jiǎn)稱Volume I
影響因子2023Vladimir Maz’ya,Serguei Nazarov,Boris A. Plamenevs
視頻videohttp://file.papertrans.cn/164/163836/163836.mp4
學(xué)科分類Operator Theory: Advances and Applications
圖書(shū)封面Titlebook: Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains; Volume I Vladimir Maz’ya,Serguei Nazarov,Boris A. Pl
影響因子.For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of elliptic boundary value problems in singularly perturbed domains. This first volume is devoted to domains whose boundary is smooth in the neighborhood of finitely many conical points. In particular, the theory encompasses the important case of domains with small holes. The second volume, on the other hand, treats perturbations of the boundary in higher dimensions as well as nonlocal perturbations. .The core of this book consists of the solution of general elliptic boundary value problems by complete asymptotic expansion in powers of a small parameter that characterizes the perturbation of the domain. The construction of this method capitalizes on the theory of elliptic boundary value problems with nonsmooth boundary that has been developed in the past thirty years. .Much attention is paid to concrete problems in mathematical physics, for example in elasticity theory. In particular, a study of the asymptotic behavior of stress intensity factors, energy integrals and eigenvalues is presented..To a large extent the book is based on the authors
Pindex Book 2000
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Asymptotics of Solutions to General Elliptic Boundary Value Problems in Domains Perturbed Near Cone ingular perturbation of the limit domain Ω whose boundary contains a finite number of cone vertices. The complete asymptotic expansions will be constructed and justified. The present chapter provides the basis for further study of special singularly perturbed boundary value problems. The general res
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Asymptotic Behaviour of Energy Integrals for Small Perturbations of the Boundary Near Corners and Iss in smoothing of the boundary in a neighborhood of the singularity, and in the second case the isolated point is transformed into a small hole. Our aim is to derive and to justify mathematically asymptotic formulas for energy functionals applied to boundary value problems for systems which are elli
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Asymptotic Behaviour of Energy Integrals for Particular Problems of Mathematical Physicsns that are disturbed near a corner or conic point and in domains with one or more small holes. The asymptotic behaviour of the energy integral for Neumann’s problem in domain with a small hole is given in 8.2, and Dirichlet’s problem for the biharmonic operator in such a domain is considered in 8.3
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Homogeneous Solutions of Boundary Value Problems in the Exterior of a Thin Coneonsider eigenvalues of polynomial operator pencils from the same point of view. Such problems arise in a natural way when we investigate singularities of solutions of boundary value problems in domains with conic points.
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