Edi Rosset

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.

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

In this paper we obtain quantitative estimates of strong unique continuation for solutions to parabolic equations. We apply these results to prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain Ω in R n , from the knowledge of overdetermined boundary data for parabolic boundary value problems.

Detecting cavities by electrostatic boundary measurements

We prove upper and lower bounds on the size of an unknown cavity, or of a perfectly conducting inclusion, in an electrical conductor in terms of boundary measurements of voltage and current. Such bounds, which might be used as a decision tool in quality testing of materials, are obtained by a nontrivial extension of previous results (Alessandrini G, Rosset E and Seo J K 2000 Proc. Am. Math. Soc. 128 53–64) regarding inclusions of finite, nonzero conductivity.

Stable determination of cavities in elastic bodies

We prove a conditional stability estimate for the inverse problem of determining either cavities inside an elastic body Ω or unknown boundary portions, from a single measurement of traction and displacement taken on the accessible part of the exterior boundary of Ω.

Numerical size estimates of inclusions in elastic bodies

We consider the problem of detecting elastic inclusions in elastic bodies by means of mechanical boundary data only, that is measurements of boundary displacement and traction. In previous work of some of the present authors, upper and lower bounds on the size (area or volume) of the inclusions were proven analytically. Following the guidelines drawn up in such previous theoretical study, an extended numerical investigation has been performed in order to prove the effectiveness of this approach. The sensitivity with respect to various relevant parameters is also analysed.

Computing Volume Bounds of Inclusions by Eit Measurements

Abstract The size estimates approach for Electrical Impedance Tomography (EIT) allows for estimating the size (area or volume) of an unknown inclusion in an electrical conductor by means of one pair of boundary measurements of voltage and current. In this paper we show by numerical simulations how to obtain such bounds for practical application of the method. The computations are carried out both in a 2-D and a 3-D setting.

Detecting an Inclusion in an Elastic Body by Boundary Measurements

We consider the problem of determining, within an elastic isotropic body

The linear constraints in Poincaré and Korn type inequalities

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Uniqueness and stability in determining a rigid inclusion in an elastic body

, the possible presence of an inclusion D made of different elastic material {from} boundary measurements of traction and displacement. We prove that the volume (size) of D can be estimated, {from} above and below, by an easily expressed quantity related to work depending only on the boundary traction and displacement.

On doubling inequalities for elliptic systems

Abstract We investigate the character of the linear constraints which are needed for Poincaré and Korn type inequalities to hold. We especially analyze constraints which depend on restriction on subsets of positive measure and on the trace on a portion of the boundary. 2000 Mathematics Subject Classification: 26D15; 35R45, 74B05.