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We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on…

Chaotic Dynamics · Physics 2009-11-07 Govindan Rangarajan , Mingzhou Ding

We prove an optimal result of stability under $\ell_p$-sums of some concentration properties for Lipschitz maps defined on Hamming graphs into Banach spaces. As an application, we give examples of spaces with Szlenk index arbitrarily high…

Functional Analysis · Mathematics 2024-11-22 Audrey Fovelle

We propose a new concept of generalized differentiation of set-valued maps that captures the first order information. This concept encompasses the standard notions of Frechet differentiability, strict differentiability, calmness and…

Optimization and Control · Mathematics 2011-01-04 C. H. Jeffrey Pang

For a bounded weak Lipschitz domain we show the so called `Maxwell compactness property', that is, the space of square integrable vector fields having square integrable weak rotation and divergence and satisfying mixed tangential and normal…

Analysis of PDEs · Mathematics 2019-01-24 Sebastian Bauer , Dirk Pauly , Michael Schomburg

The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…

Optimization and Control · Mathematics 2025-04-30 Boris S. Mordukhovich , Pengcheng Wu , Xiaoqi Yang

In [2] we characterized in terms of a quadratic growth condition various metric regularity properties of the subdifferential of a lower semicontinuous convex function acting in a Hilbert space. Motivated by some recent results in [16] where…

Optimization and Control · Mathematics 2015-07-01 Francisco J. Aragón Artacho , Michel H. Geoffroy

This paper is devoted to studying of some properties of multivalued mappings in Euclidean space. There were proved theorems on a fixed point for multivalued mappings whose restrictions to some subset in the closure of a domain satisfy "a…

Complex Variables · Mathematics 2013-10-11 Yuri Zelinskii , Maxim Tkachuk , Bogdan Klishchuk

In this paper we focus on different -- global, semi-local and local -- versions of Hoffman type inequalities expressed in a variational form. In a first stage our analysis is developed for generic multifunctions between metric spaces and we…

Optimization and Control · Mathematics 2022-03-22 Jesús Camacho , María Josefa Cánovas , Juan Parra

The Laplacian $\Delta_{\mathbb{S}^{n-1}}$ on the unit sphere $\mathbb{S}^{n-1}\subset \mathbb{R}^n$ has the property that it can explicitly be expressed in terms of $\Lambda$, the Dirichlet-to-Neumann map of the unit ball, as…

Analysis of PDEs · Mathematics 2025-10-13 Romain Speciel

In present paper, an analysis of the stability behaviour of ideal efficient solutions to parametric vector optimization problems is conducted. A sufficient condition for the existence of ideal efficient solutions to locally perturbed…

Optimization and Control · Mathematics 2021-11-02 Amos Uderzo

The usual definition of the stability region of implicit multistep methods often implies that there are some isolated points of stability within the region of instability of the numerical method. These isolated stable points may appear when…

Numerical Analysis · Mathematics 2019-01-30 Lajos Lóczi

For general set-valued mappings, the Aubin property is ultimately tied to limiting coderivatives by the Mordukhovich criterion. Likewise, the existence of single-valued Lipschitzian localizations is related to strict graphical derivatives.…

Optimization and Control · Mathematics 2026-02-06 Helmut Gfrerer , Jiri V. Outrata

It is proved that the space of differential forms with weak exterior and co-derivative, is compactly embedded into the space of square integrable differential forms. Mixed boundary conditions on weak Lipschitz domains are considered.…

Analysis of PDEs · Mathematics 2019-05-01 Sebastian Bauer , Dirk Pauly , Michael Schomburg

This paper addresses Lipschitzian stability issues that play an important role in both theoretical and numerical aspects of variational analysis, optimization, and their applications. We particularly concentrate on the so-called relaxed…

Functional Analysis · Mathematics 2019-02-27 Andrew C. Eberhard , Boris S. Mordukhovich , Janosch Rieger

The paper deals with the implicit programming approach to a class of Mathematical Programs with Equilibrium Constraints (MPECs) and bilevel programs in the case when the corresponding reduced problems are solved using a bundle method of…

Optimization and Control · Mathematics 2024-12-10 Helmut Gfrerer , Michal Kočvara , Jiří V. Outrata

We study the relaxation of multiple integrals of the calculus of variations, where the integrands are nonconvex with convex effective domain and can take the value \infty. We use local techniques based on measure arguments to prove integral…

Analysis of PDEs · Mathematics 2012-07-25 Omar Anza Hafsa , Jean Philippe Mandallena

We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…

Numerical Analysis · Mathematics 2017-08-07 F. Patricia Medina , Malgorzata Peszynska

Although the property of strong metric subregularity of set-valued mappings has been present in the literature under various names and with various definitions for more than two decades, it has attracted much less attention than its older…

Optimization and Control · Mathematics 2018-05-15 Radek Cibulka , Asen Dontchev , Alexander Kruger

Concerning the Laplace operator with homogeneous Dirichlet boundary conditions, the classical notion of isospectrality assumes that two domains are related when they give rise to the same spectrum. In two dimensions, non isometric,…

Numerical Analysis · Mathematics 2018-03-30 Lorella Fatone , Daniele Funaro

This work establishes a Lipschitz stability result for identifying unknown polygonal inclusions along with their unknown constant conductivity values, given boundary measurements encoded in the Dirichlet-to-Neumann map.

Analysis of PDEs · Mathematics 2026-05-12 Tianrui Dai