The Cauchy Problem for Solutions of Elliptic Equations (Mathematical Topics) - Hardcover

Tarkhanov, Nikolai N.

9783055016639: The Cauchy Problem for Solutions of Elliptic Equations (Mathematical Topics)

Hardcover

ISBN 10: 3055016637 ISBN 13: 9783055016639

Publisher: Vch Pub

The author aims to bring together various topics in partial differential equations related to the Cauchy problem. The problem of analytic continuation of functions given on a boundary subset is a good paradigm. Since Hadamard, the Cauchy problem for solutions of elliptic equations is known to be ill-posed. The type of instability in the problem is the same as in the simplest of analytic continuation. As it is conditionally stable, these factors determine the tools for the analysis. The study of the Cauchy problem is carried out in three directions - namely, determining the degree of instability, finding solvability conditions and reconstruction of solutions via their Cauchy data. The theory applies as well to the Cauchy problem for the solution of overdetermined elliptic systems.

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From the Publisher:

This book examines the Cauchy problem for elliptic equations under the aspects of approximation, solvability, and reconstruction of solutions via their initial data. It also explores the problem of analytic continuation of functions from a boundary subset.

About the Author:

Author's affiliation:
Nikolai N. Tarkhanov, Professor, University of Krasnoyarsk, University of Potsdam, Max Planck Research Group "Partial Differential Equations and Complex Analysis"

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