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The Cauchy Problem for Solutions of Elliptic Equations (Mathematical Topics)
The Cauchy Problem for Solutions of Elliptic Equations (Mathematical Topics)
Date: 11 June 2011, 02:35

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Product Description: 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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