First order elliptic systems : a function theoretic approach / Robert P. Gilbert, James L. Buchanan.

Format:

Book

Author/Creator:

Gilbert, Robert P., 1932-

Contributor:

Buchanan, James L.

Series:

Mathematics in science and engineering ; v. 163.

Mathematics in science and engineering ; v. 163

Language:

English

Subjects (All):

Differential equations, Elliptic.

Differential equations.

Physical Description:

1 online resource (295 p.)

Place of Publication:

New York : Academic Press, 1983.

Language Note:

English

Summary:

First order elliptic systems : a function theoretic approach

Contents:

Front Cover; First Order Elliptic Systems: A Function Theoretic Approach; Copyright Page; Contents; Preface; Chapter 0. Introduction; Chapter 1. Elliptic Systems in the Plane; 1. Introduction; 2. Hyperanalytic Functions; 3. Generalized Derivatives and the Hypercomplex Pompieu Operator; 4. Generalized Hyperanalytic Functions and Liouville's Theorem; 5. Cauchy Representation for Generalized Hyperanalytic Functions; 6. M-Analytic Functions; 7. Approximate Solutions; Chapter 2. Boundary Value Problems; 1. Introduction; 2. The Plemlj Formulas; 3. The Hilbert Problem for Hyperanalytic Functions

4. The Representation of a Piecewise Generalized Hyperanalytic Function in Terms of a Density5. The Hilbert Problem for Generalized Hyperanalytic Functions; 6. The Hilbert Problem in the Purely Hypercomplex Case; 7. The Riemann-Hilbert Problem for Hypercomplex Functions; 8. The Representation of a Generalized Hyperanalyiic Function in Terms of a Real Density; 9. The Riemann-Hilbert Problem for Generalized Hyperanalytic Functions; 10. The Riemann-Hilbert Problem in the Purely Hypercomplex Case; Chapter 3. Reductions to Hyperanalyticity; 1. Introduction; 2. Similarity Principles

3. Global Similarity Principle4. The Riemann-Hilbert Problem; 5. Hyperanalytic Functions Having Distributional Boundary Data; 6. Nonlinear Problems and Reductions to Linear Problems; 7. Liouville's Theorem and the Similarity Principle for Pascali Systems; Chapter 4. Function Theory over Clifford Algebras; 1. Introduction; 2. Regular Functions; 3. Hilbert Modules; 4. Liouville's Theorem; 5. a-Holomorphic Functions; 6. Generalized Regular Functions in Rn; 7. Overdetermined Elliptic Systems; 8. Function Theory for Higher Order Elliptic Systems with Analytic Coefficients

9. Commutative Alternatives for Higher Dimensional Function TheoryChapter 5. Partial Differential Equations of Several Complex Variables; 1. Inhomogeneous Cauchy-Riemann Equations in Polycylinders; 2. Inhomogeneous Cauchy-Riemann Systems for Several Unknowns; 3. Existence Theorems for Solutions of Partial Differential Equations in Several Complex Variables; 4. Real-Linear Equations in Two Complex Variables; 5. Nonhomogeneous Cauchy-Riemann Equations in Analytic Polyhedra; 6 . Pluriharmonic Functions; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 269-274) and index.

ISBN:

1-282-28934-9

9786612289347

0-08-095669-6

OCLC:

316566645