The Cauchy Problem for Solutions of Elliptic Equations
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The Cauchy Problem for Solutions of Elliptic Equations

The Cauchy Problem for Solutions of Elliptic Equations

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About the Book

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.

Table of Contents:
Function spaces; pseudodifferential operators in the spaces of distributions on closed sets; capacity; systems of differential equations with injective (surjective) symbol; coarse results on approximation by solutions of a system with surjective symbol; approximation in spaces of smooth functions; approximation in spaces of Holder functions; approximation in spaces of Sobolev functions; generalized boundary values of solutions of a system with injective symbol. (Part contents).


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Product Details
  • ISBN-13: 9783055016639
  • Publisher: Wiley-VCH Verlag GmbH
  • Publisher Imprint: Wiley-VCH Verlag GmbH
  • Height: 94 mm
  • Width: 66 mm
  • ISBN-10: 3055016637
  • Publisher Date: 09 May 1995
  • Binding: Hardback
  • Weight: 1090 gr


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