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Concept

Open and closed maps

Related publications (16)

Typicality results for weak solutions of the incompressible Navier-Stokes equations

Maria Colombo, Luigi De Rosa, Massimo Sorella

In this work we show that, in the class of L-infinity((0,T); L-2(T-3)) distributional solutions of the incompressible Navier-Stokes system, the ones which are smooth in some open interval of times are meagre in the sense of Baire category, and the Leray on ...

EDP SCIENCES S A2022

On the equation A del u plus (del u)(t) A = G

Bernard Dacorogna, David Valentin Strütt

Let Omega subset of R-n be an open set, A is an element of R-nxn and G : Omega -> R-nxn be given. We look for a solution u : Omega -> R-n of the equation ...

PERGAMON-ELSEVIER SCIENCE LTD2020

Geometric landscapes for material discovery within energy–structure–function maps

Berend Smit, Seyedmohamad Moosavi, Henglu Xu

Porous molecular crystals are an emerging class of porous materials formed by crystallisation of molecules with weak intermolecular interactions, which distinguishes them from extended nanoporous materials like metal–organic frameworks (MOFs). To aid disco ...

2020

Convergences of Regularized Algorithms and Stochastic Gradient Methods with Random Projections

Volkan Cevher, Junhong Lin

We study the least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space as a special case. We rst investigate regularized algorithms adapted to a projection operator on a closed subspace ...

2020

Path properties of the solution to the stochastic heat equation with Levy noise

Robert Dalang, Carsten Hao Ye Chong, Thomas Marie Jean-Baptiste Humeau

We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...

SPRINGER2019

On a generalization of the Poincaré Lemma to equations of the type dw + a ∧ w = f

David Valentin Strütt

We study the system of linear partial differential equations given by dw + a Lambda w = f, on open subsets of R-n, together with the algebraic equation da Lambda u = beta, where a is a given 1-form, f is a given (k + 1)-form, beta is a given k + 2-form, w ...

2018

On Hardy and Caffarelli-Kohn-Nirenberg inequalities

Hoài-Minh Nguyên

We establish improved versions of the Hardy and Caffarelli-Kohn-Nirenberg inequalities by replacing the standard Dirichlet energy with some nonlocal nonconvex functionals which have been involved in estimates for the topological degree of continuous maps f ...

2019

A refined estimate for the topological degree

Hoài-Minh Nguyên

We sharpen an estimate of [4] for the topological degree of continuous maps from a sphere Sdinto itself in the case d >= 2. This provides the answer for d >= 2 to a question raised by Brezis. The problem is still open for d = 1. (C) 2017 Academie des scien ...

2017

Fundamental Group And Pluridifferentials On Compact Kahler Manifolds

Yohan Cédric Loup Brunebarbe

A compact Kahler manifold X is shown to be simply connected if its 'symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective connected holomorphic m ...

Independent Univ Moscow-Ium2016

On the Richter-Thomassen Conjecture about Pairwise Intersecting Closed Curves

János Pach

A long-standing conjecture of Richter and Thomassen states that the total number of intersection points between any n simple closed Jordan curves in the plane, so that any pair of them intersect and no three curves pass through the same point, is at least ...

Cambridge Univ Press2016

Stable blow up dynamics for energy supercritical wave equations

Roland Donninger

We study the semilinear wave equation

\displaystyle \partial _t^2 \psi -\Delta \psi =\vert\psi \vert^{p-1}\psi

for

p > 3

with radial data in three spatial dimensions. There exists an explicit solution which blows up at

t=T>0

given by $\displaystyl ...

American Mathematical Society2014

Extendability of Continuous Maps Is Undecidable

We consider two basic problems of algebraic topology: the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational complexity. The extension problem is the following: Given topological space ...

Springer2014

Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line

Martins Bruveris

In this article we study Sobolev metrics of order one on diffeomorphism groups on the real line. We prove that the space equipped with the homogeneous Sobolev metric of order one is a flat space in the sense of Riemannian geometry, as it is isometric to an ...

Springer Verlag2014

Closedness of the Tangent Spaces to the Orbits of Proper Actions

Madeleine Jotz

In this note we show that, for any proper action of a Banach-Lie group G on a Banach manifold M, the corresponding tangent maps g -> T-x(M) have closed range for each x is an element of M, i.e., the tangent spaces of the orbits are closed. As a consequence ...

2008

Some applications of symmetries in differential geometry and dynamical systems

Oana Mihaela Dragulete

This thesis deals with applications of Lie symmetries in differential geometry and dynamical systems. The first chapter of the thesis studies the singular reduction of symmetries of cosphere bundles, the conservation properties of contact systems and their ...

EPFL2007

Global continuation for ODE systems over the half-line and study of von Kármán's swirling flow problem

Gilles Evéquoz

This work is concerned with the global continuation for solutions (λ,u,ξ) ∈ R × C1{0}([0,∞), RN) × Rk of the following system of ordinary differential equations: where F: [0,∞) × RN × U × J → RN and φ: U × J → X1, for some open sets J ⊂ R and U ⊂ Rk, and w ...