## The second order pullback equation

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 discusses the possibility of choosing the map phi as the gradient of a function Phi : R-n -> R. We show that this is a very rare event unless the two forms are constant.

Published in:
Calculus Of Variations And Partial Differential Equations, 49, 1-2, 583-611
Year:
2014
Publisher:
New York, Springer
ISSN:
0944-2669
Laboratories: