Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains

SET
1. Auflage 2000
ISBN: 978-3-7643-2964-8
Verlag: Springer

Buch, Englisch, Band 111/112, 758 Seiten, Gewicht: 1770 g

Reihe: Operator Theory: Advances and Applications

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.

Zielgruppe

Research

Autoren/Hrsg.

Maz'ya, Vladimir

Nazarov, Serguei

Plamenevskij, Boris

Weitere Mitwirkende

Plamenevskij, B.

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Technische Thermodynamik
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Thermodynamik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure