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.
Citation
Olivier Kneuss. "A sharp estimate for the Jacobian equation." Differential Integral Equations 27 (11/12) 1013 - 1024, November/December 2014. https://doi.org/10.57262/die/1408366782
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