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In this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement and its normal derivative at the boundary of…

Analysis of PDEs · Mathematics 2011-11-03 Antonino Morassi , Edi Rosset , Sergio Vessella

The classical Calder\'on problem with partial data is known to be log-log stable in some special cases, but even the uniqueness problem is open in general. We study the partial data stability of an analogous inverse fractional conductivity…

Analysis of PDEs · Mathematics 2025-05-27 Giovanni Covi , Antti Kujanpää , Jesse Railo

We are concerned with the structural stability of conical shocks in the three-dimensional steady supersonic flows past Lipschitz perturbed cones whose vertex angles are less than the critical angle. The flows under consideration are…

Analysis of PDEs · Mathematics 2021-05-25 Gui-Qiang G. Chen , Jie Kuang , Yongqian Zhang

In this paper we consider the stability issue for the inverse problem of determining an unknown inclusion contained in an elastic body by all the pairs of measurements of displacement and traction taken at the boundary of the body. Both the…

Analysis of PDEs · Mathematics 2016-10-06 Antonino Morassi , Edi Rosset

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 $\Sigma$ of the boundary. Motivated by the uniqueness result for…

Analysis of PDEs · Mathematics 2023-03-31 Giovanni Alessandrini , Romina Gaburro , Eva Sincich

We are interested in the identification of a Generalized Impedance Boundary Condition from the far--fields created by one or several incident plane waves at a fixed frequency. We focus on the particular case where this boundary condition is…

Numerical Analysis · Mathematics 2013-07-23 Laurent Bourgeois , Nicolas Chaulet , Houssem Haddar

We derive Lipschitz stability estimates for the Hausdorff distance of polygonal conductivity inclusions in terms of the Dirichlet-to-Neumann map.

Analysis of PDEs · Mathematics 2020-02-13 Elena Beretta , Elisa Francini

Charged colloidal crystals exhibit a subtle interplay between electrostatic screening and elastic deformation. In an anisotropic elastic medium the coupling between dilation and the local ionic environment becomes direction dependent,…

Soft Condensed Matter · Physics 2026-04-21 Hao Wu , Zhong-Can Ou-Yang

Calder\'on's inverse conductivity problem has, so far, only been subject to conditional logarithmic stability for infinite-dimensional classes of conductivities and to Lipschitz stability when restricted to finite-dimensional classes.…

Analysis of PDEs · Mathematics 2026-02-18 Henrik Garde , Markus Hirvensalo , Nuutti Hyvönen

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…

Analysis of PDEs · Mathematics 2025-01-22 Luca Rondi , Eva Sincich , Mourad SIni

We study in this paper stability estimates for the fault inverse problem. In this problem, faults are assumed to be planar open surfaces in a half space elastic medium with known Lam\'e coefficients. A traction free condition is imposed on…

Analysis of PDEs · Mathematics 2019-07-24 Faouzi Triki , Darko Volkov

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…

Analysis of PDEs · Mathematics 2011-07-27 V. Bacchelli , M. Di Cristo , E. Sincich , S. Vessella

In this paper, we study the stability of the inverse conductivity problem of determining a convex polyhedral inclusion embedded in a homogeneous isotropic medium from a single boundary measurement. The main tools in our analysis are…

Analysis of PDEs · Mathematics 2026-05-19 Chun-Hsiang Tsou

We derive a simple criterion that ensures uniqueness, Lipschitz stability and global convergence of Newton's method for the finite dimensional zero-finding problem of a continuously differentiable, pointwise convex and monotonic function.…

Numerical Analysis · Mathematics 2022-12-13 Bastian Harrach

For linearized Navier-Stokes equations, we consider an inverse source problem of determining a spatially varying divergence-free factor. We prove the global Lipschitz stability by interior data over a time interval and velocity field at…

Analysis of PDEs · Mathematics 2021-07-12 O. Y. Imanuvilov , M. Yamamoto

This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion $\tau(t)$ of the state trajectory. For a system $\dot{r}(t)=Ar(t)$ where $A$ is invertible, we show that (1) if there exists a…

Optimization and Control · Mathematics 2020-01-07 Yuxin Wang , Huafei Sun , Yueqi Cao , Shiqiang Zhang

For unipolar hydrodynamic model of semiconductor device represented by Euler-Poisson equations, when the doping profile is supersonic, the existence of steady transonic shock solutions and C-smooth steady transonic solutions for…

Analysis of PDEs · Mathematics 2022-02-09 Yue-Hong Feng , Ming Mei , Guojing Zhang

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…

Analysis of PDEs · Mathematics 2025-08-11 Andrea Aspri , Elena Beretta , Elisa Francini , Antonino Morassi , Edi Rosset , Eva Sincich , Sergio Vessella

This paper is devoted to the proof of Lipschitz regularity, down to the microscopic scale, for solutions of an elliptic system with highly oscillating coefficients, over a highly oscillating Lipschitz boundary. The originality of this…

Analysis of PDEs · Mathematics 2015-04-08 Carlos Kenig , Christophe Prange

We study an inverse boundary value problem in corrosion detection. The model is based on a conductivity equation with nonlinear Robin boundary condition. We prove that the nonlinear Robin term can be identified locally from Cauchy data…

Analysis of PDEs · Mathematics 2026-05-08 David Johansson