Concept
Weak derivative
Related publications (9)
WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS
. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...
Amer Mathematical Soc2024Non-smooth solutions in incompressible fluid dynamics
This work is devoted to the study of the main models which describe the motion of incompressible fluids, namely the Navier-Stokes, together with their hypodissipative version, and the Euler equations. We will mainly focus on the analysis of non-smooth weak ...
EPFL2021On Some Weighted Stokes Problems. Application on Smagorinsky Models
Jacques Rappaz, Jonathan Rochat
In this paper we study existence and uniqueness of weak solutions for some non-linear weighted Stokes problems using convex analysis. The characteri- zation of these considered equations is that the viscosity depends on the strain rate of the velocity fiel ...
Springer2016Generalized Poisson Summation Formula for Tempered Distributions
The Poisson summation formula (PSF), which relates the sampling of an analog signal with the periodization of its Fourier transform, plays a key role in the classical sampling theory. In its current forms, the formula is only applicable to a limited class ...
IEEE2015Jump-diffusions in Hilbert spaces: existence, stability and numerics
By means of an original approach, called 'method of the moving frame', we establish existence, uniqueness and stability results for mild and weak solutions of stochastic partial differential equations (SPDEs) with path-dependent coefficients driven by an i ...
2010On a class of mean fi eld solutions of the Monge problem for perfect and self-interacting systems
The Monge problem [23], [27], as reformulated by Kantorovich [19], [20] is that of the transportation, at a minimum "cost", of a given mass distribu- tion from an initial to a
final position during a given time interval. It is an optimal transport problem ...
EPFL2010Categorical Foundations for K-theory
K-Theory was originally defined by Grothendieck as a contravariant functor from a subcategory of schemes to abelian groups, known today as K0. The same kind of construction was then applied to other fields of mathematics, like spaces and (not necessarily c ...
EPFL2010Wavelets on the sphere : Implementation and approximations
Pierre Vandergheynst, Laurent Jacques
We continue the analysis of the continuous wavelet transform on the 2-sphere, introduced in a previous paper. After a brief review of the transform, we define and discuss the notion of directional spherical wavelet, i.e., wavelets on the sphere that are se ...
2002Invariant Manifolds for Weak Solutions to Stochastic Equations
Viability and invariance problems related to a stochastic equation in a Hilbert space H are studied. Finite dimensional invariant C2 submanifolds of H are characterized. We derive Nagumo type conditions and prove a regularity result: Any weak solution, whi ...
2000