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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
We study the semilinear wave equation ∂t2ψ−Δψ=∣ψ∣p−1ψ 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
