Crack Theory and Edge Singularities
By: by David Kapanadze, B.-Wolfgang Schulze
Contributors: Schulze, B.-Wolfgang
Series: Mathematics and Its Applications -- 561; Mathematics and Its Applications -- 561
Publisher: Springer Netherlands
Published: 2003
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 485
ISBN-13: 9789048163847; 9789401703239
Subjects: Functional analysis; Mathematics; Differential equations, partial; Operator theory; Global analysis
Description: The book studies boundary value problems connected with geometric singularities and models of the crack theory. New and interesting phenomena on the behaviour of solutions (regularity in weighted spaces, asymptotics) are analysed by means of parametrices obtained by inverting corresponding scalar and operator-valued symbols. Compared with other expositions in the field of crack theory and analysis on configurations with singularities the present book systematically develops for the first time an approach in terms of algebras of (pseudo-differential) boundary value problems. The calculus is decomposed into a number of simpler structures, namely boundary value problems (Chapter 1) and edge problems near the crack boundary (Chapter 4). Necessary tools on parameter-dependent cone operators (Chapter 2) and operators on spaces with conical exits to infinity (Chapter 3) are developed as theories of independent interest. The crack theory (Chapter 5) then appears as an application of the edge calculus. The book is addressed to mathematicians and physicists interested in boundary value problems, geometric singularities, asymptotic analysis, as well as to specialists in the field of crack theory and other singular models.
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