arXiv subjects

Eva Sincich

Publications and source records attributed to Eva Sincich.

At least 19 recordsLinked to original sources

arXiv2026

Identification of an inclusion from local Cauchy data for time-harmonic elastic waves

We consider the inverse problem of determining an inclusion contained in an elastic body undergoing time-harmonic oscillations at fixed frequency by local Cauchy data. Both the body and the inclusion are made by different homogeneous linearly elastic isotropic materials, with piecewise constant mass densities. Under mild a priori regularity assumptions on the unknown inclusion and with no spectral hypothesis on the frequency, we establish a logarithmic-type stability estimate by local Cauchy data. We also provide a stability result in terms of the so local Dirichlet to Neumann map for sufficiently small frequency.

math.AP↗

arXiv2026

Recovery of an Anisotropic Conductivity from the Neumann-to-Dirichlet Map in a Semilinear Elliptic Equation

We study the inverse boundary value problem of detecting a non-uniform conductivity motivated by pacing-guided ablation in cardiac electrophysiology. At the stationary level, the transmembrane potential $u$ in a region $Ω\subset\mathbb{R}^3$ of cardiac tissue satisfies \[ -\nabla\!\cdot(γ\nabla u)+αu^3=0 \quad \text{in }Ω,\qquad γ\nabla u\cdotν=g \quad \text{on }\partialΩ, \] where $γ$ is an anisotropic conductivity tensor and $α$ a nonlinear ionic response coefficient. The Neumann data $g$ represent pacing currents, and the boundary values $u|_{\partialΩ}$ correspond to invasive voltage measurements. Ischemic regions are modeled by a subdomain $D\subsetΩ$ where $γ$ is piecewise constant. We address the inverse problem of determining $γ$ from the Neumann-to-Dirichlet (NtD) map, assuming that $α$ and $D$ are known. To our knowledge, uniqueness in the case of NtD data with anisotropic conductivities in this nonlinear setting has not been analyzed in previous work. Using a first-order linearization around a nontrivial pacing current, we prove uniqueness for $γ$.

math.AP↗

arXiv2025

Lipschitz Stability for Polyhedral Elastic Inclusions from Partial Data

The paper deals with the inverse problem of determining a polyhedral inclusion compactly contained in an elastic body from boundary measurements of traction and displacement taken on an open portion of the boundary. Both the inclusion and the body are made of homogeneous isotropic material. Under suitable assumptions on the geometry of the unknown inclusion, we prove a constructive Lipschitz stability estimate from the local Dirichlet-to-Neumann map.

math.AP↗

arXiv2025

The local complex Calderón problem. Stability in a layered medium for a special type of anisotropic admittivity

We deal with Calderón's problem in a layered anisotropic medium $Ω\subset\mathbb{R}^n$, $n\geq 3$, with complex anisotropic admittivity $σ=γA$, where $A$ is a known Lipschitz matrix-valued function. We assume that the layers of $Ω$ are fixed and known and that $γ$ is an unknown affine complex-valued function on each layer. We provide Hölder and Lipschitz stability estimates of $σ$ in terms of an ad hoc misfit functional as well as the more classical Dirichlet to Neumann map localised on some open portion $Σ$ of $\partialΩ$, respectively.

math.AP↗

arXiv2025

Stable determination of a rigid scatterer in elastodynamics

We deal with an inverse elastic scattering problem for the shape determination of a rigid scatterer in the time-harmonic regime. We prove a local stability estimate of log log type for the identification of a scatterer by a single far-field measurement. The needed a priori condition on the closeness of the scatterers is estimated by the universal constant appearing in the Friedrichs inequality.

math.AP↗

arXiv2023

Determining an anisotropic conductivity by boundary measurements: stability at the boundary

We consider the inverse problem of determining, the possibly anisotropic, conductivity of a body by means of the so called local Neumann to Dirichlet map on a curved portion $Σ$ of the boundary. Motivated by the uniqueness result for piecewise constant anisotropic conductivities proved in \cite{Al-dH-G}, we provide a Hölder stability estimate on $Σ$ when the conductivity is a priori known to be a constant matrix near $Σ$.

math.AP↗

arXiv2023

Strong unique continuation and global regularity estimates for nanoplates

In this paper we analyze some properties of a sixth order elliptic operator arising in the framework of the strain gradient linear elasticity theory for nanoplates in flexural deformation. We first rigorously deduce the weak formulation of the underlying Neumann problem as well as its well posedness. Under some suitable smoothness assumptions on the coefficients and on the geometry we derive interior and boundary regularity estimates for the solution of the Neumann problem. Finally, for the case of isotropic materials, we obtain new Strong Unique Continuation results in the interior, in the form of doubling inequality and three spheres inequality, by a Carlemann estimates approach.

math.AP↗

arXiv2022

Size estimates for nanoplates

We consider the problem of determining, within an elastic isotropic nanoplate in bending, the possible presence of an inclusion made of different elastic material. Under suitable a priori assumptions on the unknown inclusion, we provide quantitative upper and lower estimates for the area of the unknown defect in terms of the works exerted by the boundary data when the inclusion is present or absent.

math.AP↗

arXiv2022

Stability for the Calderón's problem for a class of anisotropic conductivities via an ad-hoc misfit functional

We address the stability issue in Calderón's problem for a special class of anisotropic conductivities of the form $σ=γA$ in a Lipschitz domain $Ω\subset\mathbb{R}^n$, $n\geq 3$, where $A$ is a known Lipschitz continuous matrix-valued function and $γ$ is the unknown piecewise affine scalar function on a given partition of $Ω$. We define an ad-hoc misfit functional encoding our data and establish stability estimates for this class of anisotropic conductivity in terms of both the misfit functional and the more commonly used local Dirichlet-to-Neumann map.

math.AP↗

arXiv2022

Stable determination of an anisotropic inclusion in the Schrödinger equation from local Cauchy data

We consider the inverse problem of determining an inclusion contained in a body for a Schrödinger type equation by means of local Cauchy data. Both the body and the inclusion are made by inhomogeneous and anisotropic materials. Under mild a priori assumptions on the unknown inclusion, we establish a logarithmic stability estimate in terms of the local Cauchy data. In view of possible applications, we also provide a stability estimate in terms of an ad-hoc misfit functional.

math.AP↗

arXiv2021

Doubling inequality at the boundary for the Kirchhoff-Love plate's equation with supported conditions

In this article we derive a doubling inequality at the boundary for solutions to the Kirchhoff-Love isotropic plate's equation satisfying supported boundary conditions. To this end, we combine the use of a suitable conformal mapping which flattens the boundary and a reflection argument which guarantees the needed regularity of the extended solution. We finally apply inequalities of Carleman type in order to derive the result. The latter implies Strong Unique Continuation Property at the boundary (SUCPB).

math.AP↗

arXiv2020

Full Reciprocity-Gap Waveform Inversion in the frequency domain, enabling sparse-source acquisition

The quantitative reconstruction of sub-surface Earth properties from the propagation of waves follows an iterative minimization of a misfit functional. In marine seismic exploration, the observed data usually consist of measurements of the pressure field but dual-sensor devices also provide the normal velocity. Consequently, a reciprocity-based misfit functional is specifically designed, and defines the Full Reciprocity-gap Waveform Inversion (FRgWI ) method. This misfit functional provides additional features compared to the more traditional least-squares approaches with, in particular, that the observational and computational acquisitions can be different. Therefore, the positions and wavelets of the sources from which the measurements are acquired are not needed in the reconstruction procedure and, in fact, the numerical acquisition (for the simulations) can be arbitrarily chosen. Based on three-dimensional experiments, FRgWI is shown to behave better than Full Waveform Inversion (FWI) in the same context. Then, it allows for arbitrary numerical acquisitions in two ways: when few measurements are given, a dense numerical acquisition (compared to the observational one) can be used to compensate. On the other hand, with a dense observational acquisition, a sparse computational one is shown to be sufficient, for instance with multiple-point sources, hence reducing the numerical cost. FRgWI displays accurate reconstructions in both situations and appears more robust with respect to cross-talk than the least-squares shot-stacking.

physics.geo-ph↗

arXiv2020

On Runge approximation and Lipschitz stability for a finite-dimensional Schrödinger inverse problem

In this note we reprove the Lipschitz stability for the inverse problem for the Schrödinger operator with finite-dimensional potentials by using quantitative Runge approximation results. This provides a quantification of the Schrödinger version of the argument from Kohn and Vogelius in Comm. Pure Appl. Math. (1985) and presents a slight variant of the strategy considered by Alessandrini, de Hoop, Gaburro and Sincich in Asymptotic Analysis (2018) which may prove useful also in the context of more general operators.

math.AP↗

arXiv2018

Inverse problem for the Helmholtz equation with Cauchy data: reconstruction with conditional well-posedness driven iterative regularization

In this paper, we study the performance of Full Waveform Inversion (FWI) from time-harmonic Cauchy data via conditional well-posedness driven iterative regularization. The Cauchy data can be obtained with dual sensors measuring the pressure and the normal velocity. We define a novel misfit functional which, adapted to the Cauchy data, allows the independent location of experimental and computational sources. The conditional well-posedness is obtained for a hierarchy of subspaces in which the inverse problem with partial data is Lipschitz stable. Here, these subspaces yield piecewise linear representations of the wave speed on given domain partitions. Domain partitions can be adaptively obtained through segmentation of the gradient. The domain partitions can be taken as a coarsening of an unstructured tetrahedral mesh associated with a finite element discretization of the Helmholtz equation. We illustrate the effectiveness of the iterative regularization through computational experiments with data in dimension three. In comparison with earlier work, the Cauchy data do not suffer from eigenfrequencies in the configurations.

math.AP↗

arXiv2018

Lipschitz stability for the Finite Dimensional Fractional Calderón Problem with Finite Cauchy Data

In this note we discuss the conditional stability issue for the finite dimensional Calderón problem for the fractional Schrödinger equation with a finite number of measurements. More precisely, we assume that the unknown potential $q \in L^{\infty}(Ω) $ in the equation $((-Δ)^s+ q)u = 0 \mbox{ in } Ω\subset \mathbb{R}^n$ satisfies the a priori assumption that it is contained in a finite dimensional subspace of $L^{\infty}(Ω)$. Under this condition we prove Lipschitz stability estimates for the fractional Calderón problem by means of finitely many Cauchy data depending on $q$. We allow for the possibility of zero being a Dirichlet eigenvalue of the associated fractional Schrödinger equation. Our result relies on the strong Runge approximation property of the fractional Schrödinger equation.

math.AP↗

arXiv2017

EIT in a layered anisotropic medium

We consider the inverse problem in geophysics of imaging the subsurface of the Earth in cases where a region below the surface is known to be formed by strata of different materials and the depths and thicknesses of the strata and the (possibly anisotropic) conductivity of each of them need to be identified simultaneously. This problem is treated as a special case of the inverse problem of determining a family of nested inclusions in a medium $Ω\subset\mathbb{R}^n$, $n \geq 3$.

math.AP↗

arXiv2017

Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data

We consider the inverse boundary value problem of determining the potential $q$ in the equation $Δu + qu = 0$ in $Ω\subset\mathbb{R}^n$, from local Cauchy data. A result of global Lipschitz stability is obtained in dimension $n\geq 3$ for potentials that are piecewise linear on a given partition of $Ω$. No sign, nor spectrum condition on $q$ is assumed, hence our treatment encompasses the reduced wave equation $Δu + k^2c^{-2}u=0$ at fixed frequency $k$.

math.AP↗

arXiv2016

Wave equation with Robin condition, quantitative estimates of strong unique continuation at the boundary

The main result of the present paper consists in a quantitative estimate of unique continuation at the boundary for solutions to the wave equation. Such estimate is the sharp quantitative counterpart of the following strong unique continuation property: let $u$ be a solution to the wave equation that satisfies an homogeneous Robin condition on a portion $S$ of the boundary and the restriction of $u_{\mid S}$ on $S$ is flat on a segment $\{0\}\times J$ with $0\in S$ then $u_{\mid S}$ vanishes in a neighborhood of $\{0\}\times J$.

math.AP↗