Geometry in Partial Differential Equations

By: A Pràstaro (Editor), Th M Rassias (Editor)

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Hardcover | 1 December 1993

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476 Pages

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22.86 x 16.51 x 2.54

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This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence to partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of super-manifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Topology Geometry Differential & Riemannian Geometry Booktopia Publisher Services World Scientific Publishing

Preface
Some Applications of the Coarea Formula to Partial Differential Equations	p. 1
Large Solutions for the Equation of Surfaces of Prescribed Mean Curvature	p. 18
Optical Hamiltonian Functions	p. 32
On the Geometry of the Hodge-de Rham Laplace Operators	p. 51
Minimal Surfaces in Economic Theory	p. 68
The Morimoto Problem	p. 91
Asymptotic Expansions in Spectral Geometry	p. 100
Deformations and Recursion Operators for Evolution Equations	p. 114
Geometric Hamiltonian Forms for the Kadomtsev-Petviashvili and Zabolotskaya-Khokhlov Equations	p. 155
Classification of Mixed Type Monge-Ampere Equations	p. 173
Non-Holonomic Filtration: Algebraic and Geometric Aspects of Non-Integrability	p. 189
Spencer Cohomologies	p. 215
Hawking's Radiation via Fourier Integral Operators	p. 253
Geometry of Super PDE's	p. 259
On a Geometric Approach to an Equation of J. d'Alembert	p. 316
Geometric Prequantization of the Einstein's Vacuum Field Equations	p. 323
On Differential Equations and Cartan's Projective Connections	p. 329
Smooth Marginal Analysis of Bifurcation of Extremals	p. 345
On the Schrodinger Equation for an N-Electron Atom	p. 376
Higher Symmetries and Conservation Laws of Euler-Darboux Equations	p. 389
Strings and Membranes	p. 423
Methods for Solving Two-Dimensional Nonstationary MHD Equations at Small Alfven-Mach Numbers	p. 446
Author Index	p. 465
Table of Contents provided by Blackwell. All Rights Reserved.

Geometry in Partial Differential Equations

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