Increased stability in the Cauchy problem for some elliptic equations
نویسنده
چکیده
We derive some bounds which can be viewed as an evidence of increasing stability in the Cauchy Problem for the Helmholtz equation with lower order terms when frequency is growing. These bounds hold under certain (pseudo)convexity properties of the surface where the Cauchy data are given and of variable zero order coefficient of the Helmholtz equation. Proofs use Carleman estimates, the theory of elliptic and hyperbolic boundary value problems in Sobolev spaces, and Fourier analysis. We outline open problems and possible future developments.
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