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Partial Differential and Integral Equations

  • Book
  • © 1999

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Editors:
  1. Heinrich G. W. Begehr

    1. Freie Universität Berlin, Berlin, Germany

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  2. Robert P. Gilbert

    1. University of Delaware, Newark, USA

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  3. Guo-Chun Wen

    1. Peking University, Beijing, China

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Part of the book series: International Society for Analysis, Applications and Computation (ISAA, volume 2)

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Table of contents (27 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Gauss-Manin Connexion of Curve Singularities

    • A. G. Aleksandrov
    Pages 1-22

  3. Group Convolution Operators on Step of Two Nilpotent Lie Groups

    • N. L. Vasilevski
    Pages 23-35

  4. Some Boundary Value Problems for Second Order Overdetermined Elliptic Systems in the Unit Ball Of ℂ N

    • Abduhamid Dzhuraev
    Pages 37-57

  5. Riemann-Hilbert Boundary Value Problems in ℂ N

    • Heinrich Begehr
    Pages 59-84

  6. The Riemann-Hilbert Problem for Nonlinear Elliptic Complex Equations of First Order in Multiply Connected Infinite Domains

    • Guo-Chun Wen
    Pages 85-95

  7. The Riemann-Hilbert Problem for First Order Complex Equations of Mixed Type

    • Guo-Chun Wen
    Pages 97-105

  8. On Totally Real Non-Compact Manifolds Globally Foliated by Analytic Discs

    • Elias Wegert, Georgi Khimchiachvili, Ilya Spikovsky
    Pages 107-123

  9. Boundary Behaviour of Vector-Valued Functions of Two Classes in Locally Convex Spaces

    • Chuan-Gan Hu, Ya-Hua Wang
    Pages 125-133

  10. On Singular Integrals of the Time-Harmonic Maxwell Equations Theory

    • Reynaldo Rocha-Chávez, Michael Shapiro
    Pages 135-153

  11. Systems of First Order Partial Differential Equations — A Hypercomplex Approach

    • Heinrich Begehr
    Pages 155-175

  12. To Elliptic Theory for Domains with Piecewise Smooth Boundary in the Plane

    • Alexandre P. Soldatov
    Pages 177-186

  13. Boundary Value Problems for a System of First Order Equations of a Principal Type in the Plane

    • N. Zhura
    Pages 187-191

  14. The Stability of the Riemann Boundary Value Problem for Vector Valued M-Analytic Functions

    • Chuan-Gan Hu, Dan-Ping Zhang
    Pages 193-205

  15. A Class of Inverse Hilbert Boundary Value Problems

    • Shi Qiang Liu
    Pages 207-210

  16. Cauchy Formula, Integral of Cauchy Type and Hilbert Problem for Bianalytic Functions

    • Zhao Zhen
    Pages 211-218

  17. On Uniqueness Conditions for Entire Polyharmonic Functions

    • M. B. Balk, M. Ya. Mazalov
    Pages 219-232

  18. Bi-Analytic Functions and their Applications in Elasticity

    • Wei Lin, Yuqiu Zhao
    Pages 233-247

  19. Effect of Periodic Gasket on a Periodic Contact Problem

    • Xing Li
    Pages 249-254

  20. Singular Integral Operators and Singular Quadrature Operators for Singular Integral Equations with Hilbert Kernel

    • Jinyuan Du
    Pages 255-266
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Keywords

About this book

This volume of the Proceedings of the congress ISAAC '97 collects the con­ 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 anal­ ysis are studied which are applied to the time-harmonic Maxwell equations.

Editors and Affiliations

  • Freie Universität Berlin, Berlin, Germany

    Heinrich G. W. Begehr

  • University of Delaware, Newark, USA

    Robert P. Gilbert

  • Peking University, Beijing, China

    Guo-Chun Wen

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