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Related papers: Local Lipschitz Stability for Inverse Robin Proble…

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We establish Lipschitz stability properties for a class of inverse problems. In that class, the associated direct problem is formulated by an integral operator Am depending non-linearly on a parameter m and operating on a function u. In the…

Numerical Analysis · Mathematics 2023-02-27 Darko Volkov

We prove local solvability and stability of the inverse Robin-Regge problem in the general case, taking eigenvalue multiplicities into account. We develop the new approach based on the reduction of this inverse problem to the recovery of…

Spectral Theory · Mathematics 2025-08-22 Xiao-Chuan Xu , Natalia Pavlovna Bondarenko

In this paper we present a general tool to handle the presence of zero dynamics which are asymptotically but not locally exponentially stable in problems of robust nonlinear stabilization by output feedback. We show how it is possible to…

Optimization and Control · Mathematics 2008-10-03 L. Marconi , L. Praly , A. Isidori

In this paper, we consider the inverse problem of detecting a corrosion coefficient between two layers of a conducting medium from the Neumann-to-Dirichlet map. This inverse problem is motivated by the description of the index of corrosion…

Numerical Analysis · Mathematics 2019-04-08 Bastian Harrach , Houcine Meftahi

In this short paper we prove a global logarithmic stability of the Cauchy problem for H 2-solutions of an anisotropic elliptic equation in a Lip-schitz domain. The result we obtained is based on tools borrowed from the existing technics to…

Analysis of PDEs · Mathematics 2019-03-05 Mourad Choulli

The paper investigates stability properties of solutions of optimal control problems for semilinear parabolic partial differential equations. H\"older or Lipschitz dependence of the optimal solution on perturbations are obtained for…

Optimization and Control · Mathematics 2025-11-18 Alberto Domínguez Corella , Nicolai Jork , Vladimir M. Veliov

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…

Analysis of PDEs · Mathematics 2026-05-18 Minghui Bi , Yixian Gao

We consider a parabolic equation whose coefficients are Log-Lipschitz continuous in $t$ and Lipschitz continuous in $x$. Combining a recent conditional stability result with a well posed variational problem, we reconstruct the initial…

Analysis of PDEs · Mathematics 2024-06-25 Daniele Del Santo , Martino Prizzi

Let $n\ge2$ and $\Omega$ be a bounded Lipschitz domain in $\mathbb{R}^n$. In this article, the authors investigate global (weighted) estimates for the gradient of solutions to Robin boundary value problems of second order elliptic equations…

Analysis of PDEs · Mathematics 2020-03-18 Sibei Yang , Dachun Yang , Wen Yuan

We start presenting an $L^{\infty}$-gradient bound for solutions to non-homogeneous $p$-Laplacean type systems and equations, via suitable non-linear potentials of the right hand side. Such a bound implies a Lorentz space characterization…

Analysis of PDEs · Mathematics 2015-05-14 Frank Duzaar , Giuseppe Mingione

We establish Lipschitz stability for both the potential and the initial conditions from a single boundary measurement in the context of a hyperbolic boundary initial value problem. In our setting, the initial conditions are allowed to…

Analysis of PDEs · Mathematics 2025-11-25 Shiqi Ma

In this study, we address the inverse problem of recovering the Lam\'e parameters ($\lambda, \mu$) and the density $\rho$ of a medium from the Neumann-to-Dirichlet map for any dimension $d\geq 2$. This inverse problem finds its motivation…

Optimization and Control · Mathematics 2025-05-09 Houcine Meftahi , Chayma Nssibi

In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…

Analysis of PDEs · Mathematics 2026-03-11 Kuang Huang , Bangti Jin , Yavar Kian , Faouzi Triki

In this paper, we investigate a discrete inverse problem of determining three unknowns, i.e. initial displacement, initial velocity and random source term, in a fully discrete approximation of one-dimensional stochastic hyperbolic equation.…

Analysis of PDEs · Mathematics 2026-05-13 Bin Wu , Xu Zhu , Wenwen Zhou , Zewen Wang

This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…

Optimization and Control · Mathematics 2016-08-23 B. S. Mordukhovich , M. E. Sarabi

In this work, we consider the inverse problem of simultaneously recovering two classes of quasilinear terms appearing in a parabolic equation from boundary measurements. It is motivated by several industrial and scientific applications,…

Analysis of PDEs · Mathematics 2024-12-10 Jason Choy , Yavar Kian

We show in this paper a Lipschitz stability result for a crack inverse problem in half space. The direct problem is a Laplace equation with zero Neumann condition on the top boundary. The forcing term is a discontinuity across the crack.…

Analysis of PDEs · Mathematics 2021-09-01 Darko Volkov , Yulong Jiang

This work addresses an inverse problem for a semi-discrete parabolic equation, consisting of identifying the right-hand side of the equation from solution measurements at an intermediate time and within a spatial subdomain. We apply this…

Analysis of PDEs · Mathematics 2025-10-10 Rodrigo Lecaros , Juan López-Ríos , Ariel A. Pérez

In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…

Analysis of PDEs · Mathematics 2024-02-02 Raul K. C. Araújo , Enrique Fernández-Cara , Diego A. Souza

We establish a Lipschitz stability inequality for the problem of determining the nonlinear term in a quasilinear elliptic equation by boundary measurements. We give a proof based on a linearization procedure together with special solutions…

Analysis of PDEs · Mathematics 2022-11-28 Mourad Choulli