D V Kapanadze

(Author)

Crack Theory and Edge Singularities (2003)Hardcover - 2003, 30 September 2003

Crack Theory and Edge Singularities (2003)
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Part of Series
Mathematics and Its Applications
Part of Series
Mathematics and Its Applications (Closed)
Print Length
485 pages
Language
English
Publisher
Springer
Date Published
30 Sep 2003
ISBN-10
1402015240
ISBN-13
9781402015243

Description

Boundary value problems for partial differential equations playa crucial role in many areas of physics and the applied sciences. Interesting phenomena are often connected with geometric singularities, for instance, in mechanics. Elliptic operators in corresponding models are then sin- gular or degenerate in a typical way. The necessary structures for constructing solutions belong to a particularly beautiful and ambitious part of the analysis. Cracks in a medium are described by hypersurfaces with a boundary. Config- urations of that kind belong to the category of spaces (manifolds) with geometric singularities, here with edges. In recent years the analysis on such (in general, stratified) spaces has become a mathematical structure theory with many deep relations with geometry, topology, and mathematical physics. Key words in this connection are operator algebras, index theory, quantisation, and asymptotic analysis. Motivated by Lame's system with two-sided boundary conditions on a crack we ask the structure of solutions in weighted edge Sobolov spaces and subspaces with discrete and continuous asymptotics. Answers are given for elliptic sys- tems in general. We construct parametrices of corresponding edge boundary value problems and obtain elliptic regularity in the respective scales of weighted spaces. The original elliptic operators as well as their parametrices belong to a block matrix algebra of pseudo-differential edge problems with boundary and edge conditions, satisfying analogues of the Shapiro-Lopatinskij condition from standard boundary value problems. Operators are controlled by a hierarchy of principal symbols with interior, boundary, and edge components.

Product Details

Authors:
D V KapanadzeBert-Wolfgang Schulze
Book Edition:
2003
Book Format:
Hardcover
Country of Origin:
US
Date Published:
30 September 2003
Dimensions:
24.74 x 16.76 x 2.59 cm
ISBN-10:
1402015240
ISBN-13:
9781402015243
Language:
English
Location:
Dordrecht
Pages:
485
Publisher:
Weight:
1043.26 gm

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