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Complex Methods for Partial Differential Equations
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The book contains review chapters as well as state-of-the-art research chapters on topics ranging from complex elliptic first-order systems and second-order systems with regular or singular coefficients to overdetermined systems in several complex variables and partial differential equations in Clifford analysis. Different boundary value problems are studied. Applications to crack problems in elasticity theory to cusped bars, plates, and shells are given. Wavelet transformations are constructed in Banach spaces and used to identify complex analysis from the viewpoint of geometry. Fixed-point problems, even in abstract Banach spaces, are investigated with respect to an optimal domain of existence for the solution. Audience: Researchers working in the field as well as scientists interested in the applications.
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