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We prove identification of coefficients up to gauge by Cauchy data at the boundary for elliptic systems on oriented compact surfaces with boundary or domains of $\mathbb{C}$. In the geometric setting, we fix a Riemann surface with boundary,…

Analysis of PDEs · Mathematics 2011-05-24 Pierre Albin , Colin Guillarmou , Leo Tzou , Gunther Uhlmann

In this paper we establish a global Carleman estimate for the fourth order Schr\"odinger equation posed on a $1-d$ finite domain. The Carleman estimate is used to prove the Lipschitz stability for an inverse problem consisting in retrieving…

Analysis of PDEs · Mathematics 2013-12-18 Chuang Zheng

In this note we reprove the Lipschitz stability for the inverse problem for the Schr\"odinger operator with finite-dimensional potentials by using quantitative Runge approximation results. This provides a quantification of the Schr\"odinger…

Analysis of PDEs · Mathematics 2020-02-24 Angkana Rüland , Eva Sincich

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

We consider families of multimodal interval maps with polynomial growth of the derivative along the critical orbits. For these maps Bruin and Todd have shown the existence and uniqueness of equilibrium states for the potential…

Dynamical Systems · Mathematics 2009-11-13 Jorge Milhazes Freitas , Mike Todd

This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…

Dynamical Systems · Mathematics 2016-12-12 David J. W. Simpson

We study the orbital stability and instability of single-spike bound states of semiclassical nonlinear Schrodinger (NLS) equations with critical exponent, linear and nonlinear optical lattices (OLs). These equations may model…

Analysis of PDEs · Mathematics 2010-06-25 Tai-Chia Lin , Juncheng Wei , Wei Yao

In this article, we study stability estimates when recovering magnetic fields and electric potentials in a simply connected open subset in $R^n$ with $n \geq 3$, from measurements on open subsets of its boundary. This inverse problem is…

Analysis of PDEs · Mathematics 2020-09-29 L. Potenciano-Machado , A. Ruiz , L. Tzou

In this work we study the phenomenon of increasing stability in the inverse boundary value problem for the Schr\"odinger equation. This problem was previously considered by Isakov in which he discussed the phenomenon in different ranges of…

Analysis of PDEs · Mathematics 2013-02-06 V Isakov , S Nagayasu , G Uhlmann , J-N Wang

We show that the knowledge of the set of the Cauchy data on the boundary of a $C^1$ bounded open set in $\R^n$, $n\ge 3$, for the Schr\"odinger operator with continuous magnetic and bounded electric potentials determines the magnetic field…

Analysis of PDEs · Mathematics 2012-07-10 Katsiaryna Krupchyk , Gunther Uhlmann

We study the inverse problem of identifying a periodic potential perturbation of the Dirichlet Laplacian acting in an infinite cylindrical domain, whose cross section is assumed to be bounded. We prove log-log stable determination of the…

Analysis of PDEs · Mathematics 2016-01-21 Mourad Choulli , Yavar Kian , Eric Soccorsi

In this paper we study the $p$-Poisson equation with Robin boundary conditions, where the Robin parameter is a function. By means of some weighted isoperimetric inequalities, we provide various sharp bounds for the solutions to the problems…

Analysis of PDEs · Mathematics 2022-11-22 Vincenzo Amato , Francesco Chiacchio , Andrea Gentile

We establish several quantitative stability estimates for optimal transport maps between non-degenerate densities on uniformly convex domains for the quadratic cost. Under H\"older regularity assumptions, we prove Lipschitz $L^2$…

Analysis of PDEs · Mathematics 2026-05-26 F. -U. Caja-Lopez , Matias G. Delgadino , Jun Kitagawa

We study the expanding properties of random perturbations of regular interval maps satisfying the summability condition of exponent one. Under very general conditions on the interval maps and perturbation types, we prove strong stochastic…

Dynamical Systems · Mathematics 2014-02-26 Weixiao Shen

This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…

Machine Learning · Computer Science 2009-04-07 Corinna Cortes , Mehryar Mohri , Dmitry Pechyony , Ashish Rastogi

The stability properties and perturbation-induced dynamics of the full set of stationary states of the nonlinear Schroedinger equation are investigated numerically in two physical contexts: periodic solutions on a ring and confinement by a…

Condensed Matter · Physics 2009-10-31 Lincoln D. Carr , J. Nathan Kutz , William P. Reinhardt

Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…

Dynamical Systems · Mathematics 2020-12-29 Mark A. Pinsky

This paper investigates a well-posedness property of parametric constraint systems named here Robinson stability. Based on advanced tools of variational analysis and generalized differentiation, we derive first-order and second-order…

Optimization and Control · Mathematics 2016-12-02 Helmut Gfrerer , Boris Mordukhovich

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 prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof which is essentially based…

Analysis of PDEs · Mathematics 2015-06-03 Mourad Bellassoued , Mourad Choulli , Aymen Jbalia