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

Published New York : Academic Press, 1983

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Description 1 online resource (xi, 281 pages) Series Mathematics in science and engineering ; v. 163 Mathematics in science and engineering ; v. 163. 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 Summary First order elliptic systems : a function theoretic approach Bibliography Includes bibliographical references (pages 269-274) and index Notes Print version record Subject Differential equations, Elliptic. MATHEMATICS -- Differential Equations -- Partial. Differential equations, Elliptic Equations différentielles elliptiques. Form Electronic book Author Buchanan, James L. ISBN 9780122832802 0122832809 9780080956695 0080956696

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