Related papers: Stability in an overdetermined problem for the Gre…
In this paper we study the inverse Laplace transform. We first derive a new global logarithmic stability estimate that shows that the inversion is severely ill-posed. Then we propose a regularization method to compute the inverse Laplace…
We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…
We consider stability and approximate reconstruction of Riemannian manifold when the finite number of eigenvalues of the Laplace-Beltrami operator and the boundary values of the corresponding eigenfunctions are given. The reconstruction can…
Hill's equation is a common model of a time-periodic system that can undergo parametric resonance for certain choices of system parameters. For most kinds of parametric forcing, stable regions in its two-dimensional parameter space need to…
We give a detailed exposition of the proof of Richter's local limit theorem in a refined form, and establish the stability of the remainder term in this theorem under small perturbations of the underlying distribution (including smoothing).…
We study the stability of randomized Taylor schemes for ODEs. We consider three notions of probabilistic stability: asymptotic stability, mean-square stability, and stability in probability. We prove fundamental properties of the…
We establish new quantitative estimates for localized finite differences of solutions to the Poisson problem for the fractional Laplace operator with homogeneous Dirichlet conditions of solid type settled in bounded domains satisfying the…
We study the problem of stabilization for the acoustic system with a spatially distributed damping. Imposing various hypotheses on the structural properties of the damping term, we identify either exponential or polynomial decay of…
Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and…
We derive some bounds which can be viewed as an evidence of increasing stability in the problem of recovering the potential coefficient in the Schr\"odinger equation from the Dirichlet-to-Neumann map in the presence of attenuation, when…
It has been known for some time that the Green's function of a planar domain can be defined in terms of the exit time of Brownian motion, and this definition has been extended to stopping times more general than exit times. In this paper,…
We consider overdetermined problems related to the fractional capacity. In particular we study $s$-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first…
We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in…
Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…
We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…
Tilt stability is a fundamental concept of variational analysis and optimization that plays a pivotal role in both theoretical issues and numerical computations. This paper investigates tilt stability of local minimizers for a general class…
This paper introduces and investigates a regularity condition in the asymptotic sense for optimization problems whose objective functions are polynomial. Under this regularity condition, the normalization argument in asymptotic analysis…
Starting from the Brock's construction of Continuous Steiner Symmetrization of sets, the problem of modifying continuously a given domain up to obtain a ball, preserving its measure and with decreasing first eigenvalue of the Laplace…
We obtain stability estimates (with explicit constants) for the near field from the far field of a radiating solution of the Helmholtz equation. These estimates are based on new bounds for Hankel functions and quantify increasing stability…
In this article, we provide a modified argument for proving conditional stability for inverse problems of determining spatially varying functions in evolution equations by Carleman estimates. Our method needs not any cut-off procedures and…