## Differential and Integral Equations

### A sharp estimate for the Jacobian equation

Olivier Kneuss

#### Abstract

In this paper we show the existence of $\varphi$ satisfying the estimate $$\|\varphi-\operatorname{id}\|_{C^{r+1,\alpha}} \leq C\|g\|_{C^{r+1,\alpha}}\|f-g\|_{C^{r,\alpha}}$$ together with the Jacobian equation $$g\circ \varphi \det\nabla \varphi=f.$$ We, moreover, prove that the previous estimate is sharp.

#### Article information

Source
Differential Integral Equations, Volume 27, Number 11/12 (2014), 1013-1024.

Dates
First available in Project Euclid: 18 August 2014