登入選單
返回Google圖書搜尋
Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains
Vladimir Maz'yaSerguei NazarovBoris Plamenevskij
其他書名
SET
出版Birkhäuser Basel, 2000-05-01
主題Mathematics / Differential Equations / GeneralMathematics / Functional AnalysisMathematics / Mathematical Analysis
ISBN37643296459783764329648
URLhttp://books.google.com.hk/books?id=dFVGAQAACAAJ&hl=&source=gbs_api
註釋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. While the first volume is devoted to perturbations of the boundary near isolated singular points, the second volume treats singularities of the boundary in higher dimensions as well as nonlocal perturbations. At the core of this work are solutions of elliptic boundary value problems by asymptotic expansion in powers of a small parameter that characterizes the perturbation of the domain. In particular, it treats the important special cases of thin domains, domains with small cavities, inclusions or ligaments, rounded corners and edges, and problems with rapid oscillations of the boundary or the coefficients of the differential operator. The methods presented here capitalize on the theory of elliptic boundary value problems with nonsmooth boundary that has been developed in the past thirty years. Moreover, a study on the homogenization of differential and difference equations on periodic grids and lattices is given. Much attention is paid to concrete problems in mathematical physics, particularly elasticity theory and electrostatics. To a large extent the work is based on the authors' work and has no significant overlap with other books on the theory of elliptic boundary value problems.