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This article studies an inverse problem for a transmission wave equation, a system where the main coefficient has a variable jump across an internal interface given by the boundary between two subdomains. The main result obtains Lipschitz…

Analysis of PDEs · Mathematics 2024-09-11 L Baudouin , A Imba , A Mercado , A Osses

We study an inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lam\'e parameters associated to a linear, isotropic fractional elasticity operator from…

Analysis of PDEs · Mathematics 2022-10-03 Giovanni Covi , Maarten de Hoop , Mikko Salo

We study an inverse boundary value problem with partial data in an infinite slab in $\mathbb{R}^{n}$, $n\geq 3$, for the magnetic Schr\"{o}dinger operator with an $L^{\infty}$ magnetic potential and an $L^{\infty}$ electric potential. We…

Analysis of PDEs · Mathematics 2013-11-12 Shitao Liu , Yang Yang

This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…

Mathematical Physics · Physics 2024-01-17 Michael V. Klibanov

We consider Laplace's equation in a periodically perforated domain with Robin boundary conditions on the holes, where the Robin coefficient is scaled proportionally to the inverse total surface area of the performations. We identify a…

Analysis of PDEs · Mathematics 2026-05-06 Giacomo Canevari , Kirill Cherednichenko , Arghir Zarnescu

This paper is concerned with an inverse obstacle problem for the Laplace's equation. The aim is to recover the constant conductivity coefficient in the equation and the boundary of a Dirichlet polygonal obstacle from a single pair of Cauchy…

Analysis of PDEs · Mathematics 2024-06-04 Xiaoxu Xu , Guanghui Hu

We establish a unique continuation property for solutions of the differential inequality $|\nabla u|\leq V|u|$, where $V$ is locally $L^n$ integrable on a domain in $\mathbb R^n$. A stronger uniqueness result is obtained if in addition the…

Analysis of PDEs · Mathematics 2025-05-05 Adam Coffman , Yifei Pan , Yuan Zhang

This article is concerned with uniqueness and stability issues for the inverse spectral problem of recovering the magnetic field and the electric potential in a Riemannian manifold from some asymptotic knowledge of the boundary spectral…

Analysis of PDEs · Mathematics 2018-10-30 Mourad Bellassoued , Mourad Choulli , Dos Santos Ferreira , Yavar Kian , Plamen Stefanov

In this paper, we investigate a shape optimization problem for the second Robin eigenvalue of the weighted Laplacian on bounded Lipschitz domains symmetric about the origin. Our main theorem states that the ball centered at the origin…

Analysis of PDEs · Mathematics 2026-02-24 Yi Gao , Kui Wang , Anqiang Zhu

On a convex bounded Euclidean domain, the ground state for the Laplacian with Neumann boundary conditions is a constant, while the Dirichlet ground state is log-concave. The Robin eigenvalue problem can be considered as interpolating…

Analysis of PDEs · Mathematics 2018-02-21 Ben Andrews , Julie Clutterbuck , Daniel Hauer

It is shown that solutions of the Neumann problem for the Poisson equation in an arbitrary convex $n$-dimensional domain are uniformly Lipschitz. Applications of this result to some aspects of regularity of solutions to the Neumann problem…

Analysis of PDEs · Mathematics 2008-11-07 Vladimir Maz'ya

We prove uniqueness in inverse acoustic scattering in the case the density of the medium has an unbounded gradient across $\Sigma\subseteq\Gamma=\partial\Omega$, where $\Omega$ is a bounded open subset of $\mathbb{R}^{3}$ with a Lipschitz…

Analysis of PDEs · Mathematics 2018-06-08 Andrea Mantile , Andrea Posilicano , Mourad Sini

In this paper, we investigate the existence and uniqueness of solutions for the following model problem, involving singularities and inhomogeneous Robin boundary conditions \begin{equation*} \left\{ \begin{array}{ll}…

Analysis of PDEs · Mathematics 2024-10-29 Mohamed El Hichami , Youssef El Hadfi

We consider the inverse boundary value problem of the simultaneous determination of the coefficients $\sigma$ and $q$ of the equation $-\mbox{div}(\sigma \nabla u)+qu = 0$ from knowledge of the so-called Neumann-to-Dirichlet map, given…

Analysis of PDEs · Mathematics 2025-05-26 Niall Donlon , Romina Gaburro

In this article, for the radiative transport equation, we study inverse problems of determining a time independent scattering coefficient or total attenuation by boundary data on the complementary sub-boundary after making one time input of…

Analysis of PDEs · Mathematics 2013-07-30 Manabu Machida , Masahiro Yamamoto

We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic…

Spectral Theory · Mathematics 2007-05-23 Michael Levitin , Leonid Parnovski

We consider an inverse boundary value problem for the Maxwell's equations with a given data assumed to be known only in accessible part $\Gamma$ of the boundary. We aim to prove an uniqueness result using the Dirichlet to Neumann map with…

Mathematical Physics · Physics 2020-07-14 Christian Daveau , Abdessatar Khelifi , Houssem Lihiou

In this paper, we give some simple counterexamples to uniqueness for the Calderon problem on Riemannian manifolds with boundary when the Dirichlet and Neumann data are measured on disjoint sets of the boundary. We provide counterexamples in…

Mathematical Physics · Physics 2015-10-23 Thierry Daudé , Niky Kamran , Francois Nicoleau

Let $\Omega=\Omega_0\setminus \overline{\Theta}\subset \mathbb{R}^n$, $n\geq 2$, where $\Omega_0$ and $\Theta$ are two open, bounded and convex sets such that $\overline{\Theta}\subset \Omega_0$ and let $\beta<0$ be a given parameter. We…

Analysis of PDEs · Mathematics 2024-10-08 Simone Cito , Gloria Paoli , Gianpaolo Piscitelli

We consider the inverse boundary value problem of recovering piecewise homogeneous elastic tensor and piecewise homogeneous mass density from a localized lateral Dirichlet-to-Neumann or Neumann-to-Dirichlet map for the elasticity equation…

Analysis of PDEs · Mathematics 2019-03-05 Cătălin I. Cârstea , Gen Nakamura , Lauri Oksanen