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Existence Of Solutions For Jacobian And Hessian Equations Under Smallness Assumptions

Related publications (34)

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The size of the sync basin revisited

Philippe René Joseph Jacquod, Robin Delabays

In dynamical systems, the full stability of fixed point solutions is determined by their basins of attraction. Characterizing the structure of these basins is, in general, a complicated task, especially in high dimensionality. Recent works have advocated t ...

Amer Inst Physics2017

Fixed Points For Bounded Orbits In Hilbert Spaces

Nicolas Monod, Maxime Gheysens

Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact a-compact groups (e.g., countabl ...

Elsevier2017

Application aux équations aux dérivées partielles d'une méthode par point fixe et le problème des deux puits

Sébastien Basterrechea

This thesis consists of two parts. The first part is about a variant of Banach's fixed point theorem and its applications to several partial differential equations (PDE's), abstractly of the form [ \mathcal Lu + \mathcal Q(u) = f.] The main result of thi ...

EPFL2015

Budgeted sensor placement for source localization on trees

Patrick Thiran, Laura Elisa Celis, Brunella Marta Spinelli

We address the problem of choosing a fixed number of sensor vertices in a graph in order to detect the source of a partially-observed diffusion process on the graph itself. Building on the definition of double resolvability we introduce a notion of vertex ...

2015

The second order pullback equation

Bernard Dacorogna, Olivier Kneuss, Gyula Csató

Let f, g be two closed k-forms over R-n. The pullback equation studies the existence of a diffeomorphism phi : R-n -> R-n such that phi*(g) = f. We prove two types of results. The first one sharpens some of the existing regularity results. The second one d ...

Springer2014

Distributed Pareto Optimization via Diffusion Strategies

Ali H. Sayed

We consider solving multi-objective optimization problems in a distributed manner by a network of cooperating and learning agents. The problem is equivalent to optimizing a global cost that is the sum of individual components. The optimizers of the individ ...

IEEE2013

Fixed points and amenability in non-positive curvature

Nicolas Monod

Consider a proper cocompact CAT(0) space X. We give a complete algebraic characterisation of amenable groups of isometries of X. For amenable discrete subgroups, an even narrower description is derived, implying Q-linearity in the torsion-free case. We est ...

Springer2013

Materials Taking a Lesson from Nature

Holger Frauenrath, Emmanuel Croisier, Liangfei Tian

Structural biomaterials with their often extraordinary properties and versatile functions are typically constructed from very limited sets of building blocks and types of supramolecular interactions. In this review we discuss how, inspired by nature's desi ...

Swiss Chemical Soc2013

The Stationary Behaviour of Fluid Limits of Reversible Processes is Concentrated on Stationary Points

Jean-Yves Le Boudec

Assume that a stochastic process can be approximated, when some scale parameter gets large, by a fluid limit (also called mean field limit", or hydrodynamic limit"). A common practice, often called the ``fixed point approximation" consists in approxima ...

2013

On Complete Completion using Types and Weights

Viktor Kuncak, Tihomir Gvero, Ivan Kuraj, Ruzica Piskac

Developing modern software applications typically involves composing functionality from existing libraries. This task is difficult because libraries may expose many methods to the developer. To help developers in such scenarios, we present a technique that ...

2012