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Higher Order Partial Differential Equations in Clifford Analysis

Effective Solutions to Problems

  • Elena Obolashvili

Part of the Progress in Mathematical Physics book series (PMP, volume 28)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Boundary Value Problems for Regular, Generalized Regular and Pluriregular Elliptic Equations

    1. Front Matter
      Pages 1-1
    2. Elena Obolashvili
      Pages 3-66
    3. Elena Obolashvili
      Pages 67-122
  3. Initial Value Problems for Regular and Pluriregular, Hyperbolic and Parabolic Equations

    1. Front Matter
      Pages 123-123
  4. Epilogue

    1. Elena Obolashvili
      Pages 171-171
  5. Back Matter
    Pages 173-178

About this book

Introduction

The most important thing is to write equations in a beautiful form and their success in applications is ensured. Paul Dirac The uniqueness and existence theorems for the solutions of boundary and initial value problems for systems of high-order partial differential equations (PDE) are sufficiently well known. In this book, the problems considered are those whose solutions can be represented in quadratures, i.e., in an effective form. Such problems have remarkable applications in mathematical physics, the mechanics of deformable bodies, electro­ magnetism, relativistic quantum mechanics, and some of their natural generalizations. Almost all such problems can be set in the context of Clifford analysis. Moreover, they can be obtained without applying any physical laws, a circumstance that gives rise to the idea that Clifford analysis itself can suggest generalizations of classical equations or new equations altogether that may have some physical content. For that reason, Clifford analysis represents one of the most remarkable fields in modem mathematics as well as in modem physics.

Keywords

Applications of Mathematics Boundary value problem Clifford Analysis Partial Differential Equations hyperbolic equation partial differential equation

Authors and affiliations

  • Elena Obolashvili
    • 1
  1. 1.Georgian Academy of SciencesA. Razmadze Mathematical InstituteTbilisiGeorgia

Bibliographic information

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