Sergio Vessella

The stability for the Cauchy problem for elliptic equations

Methods for forming thin layer barrier layer films for use in enzyme containing laminated membranes and membranes formed thereby are disclosed. The barrier layers exhibit improved acetaminophen rejection and comprise a cellulose acetate/cellulose acetate butyrate blend. The thin layer barrier membranes are formed from a plural solvent containing solution and are cured at a critical temperature of about 102 DEG -114 DEG F., most preferably at about 106 DEG F.-114 DEG F. while traveling through a circulating hot air oven. Alternatively, the membranes can be cured at room temperature or in a stagnant oven at temperatures of from room temperature to about 175 DEG C. (350 DEG F.) for a period of from about 10 minutes to 1 hour.

Stable determination of boundaries from Cauchy data

The problem of determining a portion

Determining linear cracks by boundary measurements: Lipschitz stability

\Gamma

Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates

of the boundary of a bounded planar domain

Quantitative estimates of unique continuation for parabolic equations and inverse initial-boundary value problems with unknown boundaries

\Omega

DOUBLING PROPERTIES OF CALORIC FUNCTIONS

from Cauchy data arises in several contexts, for example, such as in corrosion detection from electrostatic measurements. We investigate this severely ill-posed problem establishing logarithmic continuous dependence of

A note on an ill-posed problem for the heat equation

\Gamma

Stability estimates in an inverse problem for a three-dimensional heat equation

from Cauchy data.

Locations and strengths of point sources : stability estimates

We consider the inverse boundary value problem of crack detection in a two-dimensional electrical conductor. We prove an estimate of Lipschitz type on the continuous dependence of an unknown linear crack from the boundary measurements.

Stabilization of ill-posed Cauchy problems for parabolic equations

In this article, we review the main results concerning the issue of stability for the determination of unknown boundary portions of a thermic conducting body from Cauchy data for parabolic equations. We give detailed and self-contained proofs. We prove that such problems are severely ill-posed in the sense that under a priori regularity assumptions on the unknown boundaries, up to any finite order of differentiability, the continuous dependence of an unknown boundary from the measured data is, at best, of logarithmic type. We review the main results concerning quantitative estimates of unique continuation for solutions to second-order parabolic equations. We give a detailed proof of a Carleman estimate crucial for the derivation of the stability estimates.