Vladimir Maz'ya, Serguei Nazarov, Boris Plamenevskij

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains (eBook, PDF)

Volume I

• Format: PDF

Produktbeschreibung

For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors' work, and has no significant overlap with other books on the theory of elliptic boundary value problems.

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Produktdetails

• Verlag: Birkhäuser Basel
• Seitenzahl: 435
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783034884341
• Artikelnr.: 53164174

Inhaltsangabe

I Boundary Value Problems for the Laplace Operator in Domains Perturbed Near Isolated Singularities.- 1 Dirichlet and Neumann Problems for the Laplace Operator in Domains with Corners and Cone Vertices.- 2 Dirichlet and Neumann Problems in Domains with Singularly Perturbed Boundaries.- II General Elliptic Boundary Value Problems in Domains Perturbed Near Isolated Singularities of the Boundary.- 3 Elliptic Boundary Value Problems in Domains with Smooth Boundaries, in a Cylinder, and in Domains with Cone Vertices.- 4 Asymptotics of Solutions to General Elliptic Boundary Value Problems in Domains Perturbed Near Cone Vertices.- 5 Variants and Corollaries of the Asymptotic Theory.- III Asymptotic Behaviour of Functional on Solutions of Boundary Value Problems in Domains Perturbed Near Isolated Boundary Singularities.- 6 Asymptotic Behaviour of Intensity Factors for Vertices of Corners and Cones Coming Close.- 7 Asymptotic Behaviour of Energy Integrals for Small Perturbations of the BoundaryNear Corners and Isolated Points.- 8 Asymptotic Behaviour of Energy Integrals for Particular Problems of Mathematical Physics.- IV Asymptotic Behaviour of Eigenvalues of Boundary Value Problems in Domains with Small Holes.- 9 Asymptotic Expansions of Eigenvalues of Classic Boundary Value Problems.- 10 Homogeneous Solutions of Boundary Value Problems in the Exterior of a Thin Cone.- Comments on Parts I-IV.- Comments on Part I.- 1.- 2.- Comments on Part II.- 3.- 4.- 5.- Comments on Part III.- 6.- 7.- 8.- Comments on Part IV.- 9.- 10.- List of Symbols.- 1. Basic Symbols.- 2. Symbols for function spaces and related concepts.- 3. Symbols for functions, distributions and related concepts.- 4. Other symbols.- References.