Related papers: Lipschitz Stability for Polyhedral Elastic Inclusi…
This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a…
A novel variational formulation of layer potentials and boundary integral operators generalizes their classical construction by Green's functions, which are not explicitly available for Helmholtz problems with variable coefficients.…
We are concerned with the reconstruction of inclusions in elastic bodies based on measurements from a laboratory experiment. In doing so, we solve the inverse problem of the time-harmonic elastic wave equation, in contrast to the stationary…
We consider the problem of reconstructing inhomogeneities in an isotropic elastic body using time harmonic waves. Here we extend the so called monotonicity method for inclusion detection and show how to determine certain types of…
We show that the biharmonic Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which follow by abstract arguments using functional analysis…
We extend some known results from smooth dynamical systems to the category of Lipschitz homeomorphisms of compact metric spaces. We consider dynamical properties as robust expansiveness and structural stability allowing Lipschitz…
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…
We consider the inverse problem of finding unknown elastic parameters from internal measurements of displacement fields for tissues. The measurements are made on the entirety of a smooth domain. Since tissues can be modeled as…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
We construct a local Lipschitz graph around a soliton of the cubic focusing NLS in three dimensions on which global solutions exist, and asymptotic stability as well as scattering holds.
In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…
We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so--called Dirichlet-to-Neumann map is locally given on a non empty portion $\Gamma$ of the boundary…
Establishing Lipschitz stability estimates is crucial for ensuring the mathematical robustness of neural network (NN) approximations in machine learning (ML)-based parameter estimation, particularly in physics-informed settings. In this…
We revisit the stability issue of determining the conductivity at the boundary from the corresponding Dirichlet-to-Neumann map. We discuss both the method based on singular solutions and the one built on the localized oscillating solutions.…
The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/H\"older continuous mappings acting from a compact metric space to a normed space. To this end some extensions and generalizations of already existing…
The complete set of bounds for the technical constants of an elastic layer, plate or laminate is given. The bounds are valid in general, also for completely anisotropic bodies. They are obtained transforming the polar bounds previously…
We deal with Calder\'on's problem in a layered anisotropic medium $\Omega\subset\mathbb{R}^n$, $n\geq 3$, with complex anisotropic admittivity $\sigma=\gamma A$, where $A$ is a known Lipschitz matrix-valued function. We assume that the…
We establish a Lipschitz stability estimate for the inverse problem consisting in the determination of the coefficient $\sigma(t)$, appearing in a Dirichlet initial-boundary value problem for the parabolic equation $\partial_tu-\Delta_x…
An analytical solution in a closed form is obtained for the three-dimensional elastic strain distribution in an unlimited medium containing an inclusion with a coordinate-dependent lattice mismatch (an eigenstrain). Quantum dots consisting…
We treat the stability of determining the boundary impedance of an obstacle by scattering data, with a single incident field. A previous result by Sincich (SIAM J. Math. Anal. 38, (2006), 434-451) showed a log stability when the boundary of…