Related papers: An inverse problem for inhomogeneous Signorini obs…
In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…
We consider the problem of determining the unknown boundary values of a solution of an elliptic equation outside a bounded open set $B$ from the knowledge of the values of this solution on a boundary of an arbitrary Lipschitz bounded domain…
We consider boundary measurements for the wave equation on a bounded domain $M \subset \R^2$ or on a compact Riemannian surface, and introduce a method to locate a discontinuity in the wave speed. Assuming that the wave speed consist of an…
We give a definition for Obstacle Problems with measure data and general obstacles. For such problems we prove existence and uniqueness of solutions and consistency with the classical theory of Variational Inequalities. Continuous…
The determination of Parton Distribution Functions from a finite set of data is a typical example of an inverse problem. Inverse problems are notoriously difficult to solve, in particular when a robust determination of the uncertainty in…
We consider the anisotropic Calderon problem of recovering a conductivity matrix or a Riemannian metric from electrical boundary measurements in three and higher dimensions. In the earlier work \cite{DKSaU}, it was shown that a metric in a…
In this article we study the inverse problem of determining a semilinear term appearing in an elliptic equation from boundary measurements. Our main objective is to develop flexible and general theoretical results that can be used for…
In this paper we establish the existence of solutions for a model describing the evolution of a linearly viscoelastic body which is constrained to remain confined in a prescribed half-space. The confinement condition under consideration is…
In this paper, we discuss the uniqueness in an integral geometry problem in a strongly convex domain. Our problem is related to the problem of finding a Riemannian metric by the distances between all pairs of the boundary points. For the…
We prove an epiperimetric inequality for the thin obstacle problem, extending the pioneering results by Weiss on the classical obstacle problem (Invent. Math. 138 (1999), no. 1, 23-50). This inequality provides the means to study the rate…
We are concerned with the inverse boundary problem of determining anomalies associated with a semilinear elliptic equation of the form $-\Delta u+a(\mathbf x, u)=0$, where $a(\mathbf x, u)$ is a general nonlinear term that belongs to a…
An inverse problem is considered for an inhomogeneous Schr\"odinger equation. Assuming that the potential vanishes outside a finite interval and satisfies some other technical assumptions, one proves the uniqueness of the recovery of this…
We determine the twist in a birefringent optical fiber from measurements, at one end of the fiber, of the fiber response to an impulsive source at the same end. This is the inverse problem of determining a non-constant coefficient, of a…
In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the…
In this note we discuss the (higher) regularity properties of the Signorini problem for the homogeneous, isotropic Lam\'e system. Relying on an observation by Schumann \cite{Schumann1}, we reduce the question of the solution's and the free…
We consider the inverse problem of determining the isotropic inhomogeneous electromagnetic coefficients of the non-stationary Maxwell equations in a bounded domain of R^3, from a finite number of boundary measurements. Our main result is a…
We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship…
To understand the mechanics of a complex fluid such as a foam we propose a model experiment (a bidimensional flow around an obstacle) for which an external sollicitation is applied, and a local response is measured, simultaneously. We…
A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…