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STABLE DETERMINATION OF A BOUNDARY COEFFICIENT IN AN ELLIPTIC EQUATION
Preview AbstractWe prove a logarithmic stability estimate for a Cauchy problem associated with a second order elliptic operator. Our proof is essentially based on a Carleman estimate by A. L. Bukhgeim. This result is applied to establish a stability estimate for the inverse problem of determining a boundary coefficient (or a boundary function) by a single boundary measurement. This kind of inverse problems is motivated by the corrosion detection problem.
CONDITIONAL STABILITY IN RECONSTRUCTION OF INITIAL TEMPERATURES
Preview AbstractIn this paper, we shall present a conditional stability estimate of logarithmic rate in the reconstruction of initial temperatures.
Equidistribution estimates for eigenfunctions and eigenvalue bounds for random operators
Preview AbstractWe discuss properties of L2-eigenfunctions of Schrödinger operators and elliptic partial differential operators. The focus is set on unique continuation principles and equidistribution properties. We review recent results and announce new ones.