Increasing Stability of the Continuation for General Elliptic Equations of Second Order

摘要

We give stability estimates in the Cauchy problem for general partialdifferential equation of the elliptic type similar to the Helmholtz equation.We do not impose any (pseudo)convexity assumptions on the domain or theoperator. These conditional stability estimates are getting close to Lipschitzones when the wave number/frequency is growing. We split solution into low andhigh frequency parts and impose constraints on the high frequency part only.Proofs use energy estimates.