Differential and Integral Equations

A sharp estimate for the Jacobian equation

Olivier Kneuss

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1408366782

Mathematical Reviews number (MathSciNet)
MR3263079

Zentralblatt MATH identifier
1299.35099

Subjects
Primary: 35F30: Boundary value problems for nonlinear first-order equations

Citation

Kneuss, Olivier. A sharp estimate for the Jacobian equation. Differential Integral Equations 27 (2014), no. 11/12, 1013--1024. https://projecteuclid.org/euclid.die/1408366782


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