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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0255-0156 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

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Dirichlet and Neumann Problems for the Laplace Operator in Domains with Corners and Cone Verticesllustrates the general theory of elliptic boundary value problems in domains with cone vertices, which is briefly presented in Chapter 3. (Therefore we refrain from using expansions by the eigenfunctions of the Beltrami operator, which lead to the same results in the case of the Poisson equation.)

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Elliptic Boundary Value Problems in Domains with Smooth Boundaries, in a Cylinder, and in Domains wis. However, in contrast to the first part we consider here general elliptic boundary value problems. The reader who is interested only in concrete problems of mathematical physics may restrict himself to a superficial reading of Chapters 3–5.

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Martin Berger,Kohei Honda,Nobuko Yoshidain perturbed in the neighborhood of a corner. The necessary facts concerning behaviour of the solutions of problems of the theory of elasticity in a neighborhood of the sector vertex are put together in 8.5.

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