β Scribed by A. G. Aleksandrov (auth.), Heinrich G. W. Begehr, Robert P. Gilbert, Guo-Chun Wen (eds.)
No coin nor oath required. For personal study only.
This volume of the Proceedings of the congress ISAAC '97 collects the conΒ tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral equations and boundary value problems, 4. Partial differential equations. Most but not all of the authors have participated in the congress. Unfortunately some from Eastern Europe and Asia have not managed to come because of lack of financial support. Nevertheless their manuscripts of the proposed talks are included in this volume. The majority of the papers deal with complex methods. Among them boundary value problems in particular the Riemann-Hilbert, the Riemann (Hilbert) and related problems are treated. Boundary behaviour of vector-valued functions are studied too. The Riemann-Hilbert problem is solved for elliptic complex equations, for mixed complex equations, and for several complex variables. It is considered in a general topological setting for mappings into q;n and related to Toeplitz operators. Convolution operators are investigated for nilpotent Lie groups leading to some consequences for the null space of the tangential Cauchy Riemann operator. Some boundary value problems for overdetermined systems in balls of q;n are solved explicitly. A survey is given for the Gauss-Manin connection associated with deformations of curve singularities. Several papers deal with generalizations of analytic functions with various applications to mathematical physics. Singular integrals in quaternionic analΒ ysis are studied which are applied to the time-harmonic Maxwell equations.
Front Matter....Pages i-x
Gauss-Manin Connexion of Curve Singularities....Pages 1-22
Group Convolution Operators on Step of Two Nilpotent Lie Groups....Pages 23-35
Some Boundary Value Problems for Second Order Overdetermined Elliptic Systems in the Unit Ball Of β N ....Pages 37-57
Riemann-Hilbert Boundary Value Problems in β N ....Pages 59-84
The Riemann-Hilbert Problem for Nonlinear Elliptic Complex Equations of First Order in Multiply Connected Infinite Domains....Pages 85-95
The Riemann-Hilbert Problem for First Order Complex Equations of Mixed Type....Pages 97-105
On Totally Real Non-Compact Manifolds Globally Foliated by Analytic Discs....Pages 107-123
Boundary Behaviour of Vector-Valued Functions of Two Classes in Locally Convex Spaces....Pages 125-133
On Singular Integrals of the Time-Harmonic Maxwell Equations Theory....Pages 135-153
Systems of First Order Partial Differential Equations β A Hypercomplex Approach....Pages 155-175
To Elliptic Theory for Domains with Piecewise Smooth Boundary in the Plane....Pages 177-186
Boundary Value Problems for a System of First Order Equations of a Principal Type in the Plane....Pages 187-191
The Stability of the Riemann Boundary Value Problem for Vector Valued M -Analytic Functions....Pages 193-205
A Class of Inverse Hilbert Boundary Value Problems....Pages 207-210
Cauchy Formula, Integral of Cauchy Type and Hilbert Problem for Bianalytic Functions....Pages 211-218
On Uniqueness Conditions for Entire Polyharmonic Functions....Pages 219-232
Bi-Analytic Functions and their Applications in Elasticity....Pages 233-247
Effect of Periodic Gasket on a Periodic Contact Problem....Pages 249-254
Singular Integral Operators and Singular Quadrature Operators for Singular Integral Equations with Hilbert Kernel....Pages 255-266
Some Co-Circular Crack Problems with Cyclic Symmetry....Pages 267-276
The Oblique Derivative Problem for Nonlinear Parabolic Equations of Second Order with Measurable Coefficients in a Higher Dimensional Domain....Pages 277-286
Existence and Uniqueness for Boundary Value Contact Problems....Pages 287-301
Weakly Hyperbolic Equations β A Modern Field in the Theory of Hyperbolic Equations....Pages 303-318
Eigenvalue Problems for Elliptic Type Partial Differential Operators with Spectral Parameter Contained Linearly in Boundary Conditions....Pages 319-333
On Indefinite Nonlinear Neumann Problems....Pages 335-346
Higher Order Ordinary Differential Equations with Super-Singular Points....Pages 347-358
Applications of Methods of Integrals and Function Theory to Statistics....Pages 359-369
Partial Differential Equations; Integral Transforms, Operational Calculus; Functions of a Complex Variable; Several Complex Variables and Analytic Spaces; Real Functions
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