These proceedings concentrate on recent results in such fields of complex analysis as: complex methods for solving boundary value problems with piecewise smooth boundary data; complex methods for linear and nonlinear differential equations and systems of second order; and applications of scales of Banach spaces to initial value problems. Some problems in higher dimensions (such as the unification of global and local existence theorems for holomorphic functions and an elementary approach to Clifford analysis) are also discussed. The book places particular emphasis on the approaches to teach mathematical analysis based on interactions between complex variables and partial differential equations.
Boundary value problems of the theory of generalized analytic vectors, G.F. Manjavidze; solution of the Riemann boundary value problem with piecewise smooth boundary data for complex elliptic partial difference equations, A.S.A. Mshimba; elliptic second order equations, H. Begehr; two boundary value problems for nonlinear parabolic systems of second order equations with measurable coefficients, G.-C. Wen; on the abstract Cauchy-Kowalewski theorem, K. Asano; theorems of Cauchy-Kovalevsky and Holmgren type for abstract evolution equations in scales of locally convex spaces, M. Reissig; solution of initial value problems in associated spaces, R. Heersink and W. Tutschke; averaged evolution equations - the Kirchhoff string and its treatment in scales of Banach spaces, A. Arosio; propagation of real analyticity for weakly hyperbolic equations, S. Spagnolo; Schwarz-Christoffel mappings - symbolic computation of mapping functions for symmetric polygonal domains, W. Koepf; solving elliptic partial differential equations with MACSYMA, R.P. Gilbert and A. Wood; unification of global and local existence theorems for holomorphic functions of several complex variables, G. Fichera; the simple and the multiple-layer potential approach in n-dimensional problems, A. Cialdea; some remarks on generalizations of the one-dimensional complex analysis - hyper complex approach, M. Shapiro; an elementary approach to Clifford analysis, W. Tutschke; and other papers.