Methods and Applications of Analysis

Volume 9 (2002)

Number 3

A convex Darboux Theorem

Pages: 329 – 344

DOI: https://dx.doi.org/10.4310/MAA.2002.v9.n3.a3

Authors

Ivar Ekeland

Louis Nirenberg

Abstract

We give necessary and sufficent conditions for a smooth, generic, differential one-form w on Rⁿ to decompose into a sum w = a¹du₁ +... +a^kdu_k, where the function a ^l are positive and the u_l convex (or quasi-convex) near the origin.

Published 1 January 2002