arXiv subjects

S. Vessella

Publications and source records attributed to S. Vessella.

8 recordsLinked to original sources

arXiv2024

Stable determination of the Winkler subgrade coefficient in a nanoplate

We study the inverse problem of determining the Winkler coefficient in a nanoplate resting on an elastic foundation and clamped at the boundary. The nanoplate is described within a simplified strain gradient elasticity theory for isotropic materials, under the Kirchhoff-Love kinematic assumptions in infinitesimal deformation. We prove a global Hölder stability estimate of the subgrade coefficient by performing a single interior measurement of the transverse deflection of the nanoplate induced by a load concentrated at one point.

math.AP↗

arXiv2020

Carleman estimate for complex second order elliptic operators with discontinuous Lipschitz coefficients

In this paper, we derive a local Carleman estimate for the complex second order elliptic operator with Lipschitz coefficients having jump discontinuities. Combing the result in [BL] and the arguments in [DcFLVW], we present an elementary method to derive the Carleman estimate under the optimal regularity assumption on the coefficients.

math.AP↗

arXiv2016

Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization

In this paper we derive rigorously the derivative of the Dirichlet to Neumann map and of the Neumann to Dirichlet map of the conductivity equation with respect to movements of vertices of triangular conductivity inclusions. We apply this result to formulate an optimization problem based on a shape derivative approach.

math.AP↗

arXiv2015

Three-region inequalities for the second order elliptic equation with discontinuous coefficients and size estimate

In this paper, we would like to derive a quantitative uniqueness estimate, the three-region inequality, for the second order elliptic equation with jump discontinuous coefficients. The derivation of the inequality relies on the Carleman estimate proved in our previous work. We then apply the three-region inequality to study the size estimate problem with one boundary measurement.

math.AP↗

arXiv2015

Carleman estimate for second order elliptic equations with Lipschitz leading coefficients and jumps at an interface

In this paper we prove a local Carleman estimate for second order elliptic equations with a general anisotropic Lipschitz coefficients having a jump at an interface. Our approach does not rely on the techniques of microlocal analysis. We make use of the elementary method so that we are able to impose almost optimal assumptions on the coefficients and, consequently, the interface.

math.AP↗

arXiv2011

A parabolic inverse problem with mixed boundary data. Stability estimates for the unknown boundary and impedance

We consider the problem of determining an unaccessible part of the boundary of a conductor by mean of thermal measurements. We study a problem of corrosion where a Robin type condition is prescribed on the damaged part and we prove logarithmic stability estimate.

math.AP↗

arXiv2011

Quantitative uniqueness for elliptic equations with singular lower order terms

We use a Carleman type inequality of Koch and Tataru to obtain quantitative estimates of unique continuation for solutions of second order elliptic equations with singular lower order terms. First we prove a three sphere inequality and then describe two methods of propagation of smallness from sets of positive measure.

math.AP↗

arXiv2006

Doubling Properties of Caloric Functions

We prove local quantitative estimates of unique continuation for solutions to parabolic equations: doubling properties and two-sphere one-cylinder inequalities.

math.AP↗