Luca Rondi

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 corrosion by a single electrostatic boundary measurement

We prove an optimal stability estimate for an inverse Robin boundary value problem arising in corrosion detection by electrostatic boundary measurements.

Examples of exponential instability for inverse inclusion and scattering problems

Following a recent paper by Mandache (2001 Inverse Problems 17 1435–44), we establish a general procedure for determining the instability character of inverse problems. We apply this procedure to an elliptic inverse problem concerning the determination of inclusions in a conductor by different kinds of boundary measurements and to inverse obstacle acoustic scattering problems and we show that these problems are exponentially ill-posed.

Stable determination of a crack in a planar inhomogeneous conductor

We prove a stability estimate for the inverse problem of cracks under essentially minimal regularity assumptions on the crack and on the background conductivity.

Uniqueness and stability for the determination of boundary defects by electrostatic measurements

The inverse problem of the determination of boundary defects in a planar conductor by a nite number of electrostatic measurements on the boundary is considered. Uniqueness results and stability estimates are proved under essentially minimal regularity assumptions on the data. Finally, Lipschitz estimates for the determination of surface linear cracks are developed.

Optimal stability estimates for the determination of defects by electrostatic measurements

The stability issue for the inverse problem of the determination of interior and boundary defects in a planar inhomogeneous conductor by a finite number of electrostatic measurements on the boundary is considered. Essentially optimal stability estimates are obtained.

Regularized Transformation-Optics Cloaking for the Helmholtz Equation: From Partial Cloak to Full Cloak

We develop a very general theory on the regularized approximate invisibility cloaking for the wave scattering governed by the Helmholtz equation in any space dimensions

Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements

{N \geq 2}