Functional-analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations: Proceedings of the International Graz Workshop, Graz, Austria, 12-16 February 2001

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Helmut Florian
World Scientific, 2001 - Mathematics - 458 pages
Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today's rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations.This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell's equations, crystal optics, dynamical problems for cusped bars, and conservation laws.
 

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Contents

2 Applications of functionalanalytic and complex methods to mathematical physics
135
3 Partial complex differential equations in the plane
251
4 Complex methods in higher dimensions
339
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