Publications de Olivier Kneuss

Symplectic factorization, Darboux theorem and ellipticity

2018

Some Remarks on the Lie Derivative and the Pullback Equation for Contact Forms

Given the contact forms f and g, and the 1-form h, we discuss the existence of a vector field u verifying L-u(f)= d(u (right perpendicular) f)+ u (right perpendicular) df = h. This is closely related to the pullback equation, where we seek for a diffeomorp ...

Walter De Gruyter Gmbh2017

Optimal transport of closed differential forms for convex costs

Bernard Dacorogna, Olivier Kneuss

Let c : A(k-1) -> R+ be convex and Omega subset of R-n be a bounded domain. Let f(0) and f(1) be two closed k-forms on Omega satisfying appropriate boundary conditions. We discuss the minimization of integral(Omega) c (A) dx over a subset of (k - 1)-forms ...

Elsevier France-Editions Scientifiques Medicales Elsevier2015

Some New Results On Differential Inclusions For Differential Forms

Bernard Dacorogna, Olivier Kneuss, Saugata Bandyopadhyay

In this article we study some necessary and sufficient conditions for the existence of solutions in W-0(1,infinity) (Omega; Lambda(k)) of the differential inclusion d omega is an element of E a.e. in Omega where E subset of Lambda(k+1) is a prescribed set. ...

Amer Mathematical Soc2015

Multiple Jacobian Equations

Bernard Dacorogna, Olivier Kneuss

The existence, regularity and uniqueness of a local diffeomorphism phi satisfying g(i)(phi) det del phi = f(i) for 1

Amer Inst Mathematical Sciences2014

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

L'équation de rappel

Olivier Kneuss

In this thesis we are interested in the following problem : given two differential k–forms g and f, most of the time they will be assumed closed, on what conditions can we pullback g to f by a map φ ? In other words we ask when it is possible to solve the ...

EPFL2011

Divisibility in Grassmann algebra

Bernard Dacorogna, Olivier Kneuss

Given a k-form f and an l-form g with 0

2011

A Global Version Of The Darboux Theorem With Optimal Regularity And Dirichlet Condition

Bernard Dacorogna, Olivier Kneuss

Let n > 2 be even; r >= 1 be an integer; 0 < alpha < 1; Omega be a bounded, connected, smooth, open set in R-n; and nu be its exterior unit normal. Let f, g is an element of C-r,C-alpha((Omega) over bar; Lambda(2)) be two symplectic forms (i.e., closed and ...

2011

The Pullback Equation For Degenerate Forms

Bernard Dacorogna, Olivier Kneuss, Saugata Bandyopadhyay

We discuss the existence of a diffeomorphism phi : R-n -> R-n such that ...

2010