Published Paper
Inserted: 26 jan 2009
Last Updated: 14 jan 2010
Journal: Calc. Var. Partial Differential Equations
Volume: 36
Pages: 251-283
Year: 2009
Abstract:
We prove existence of $u\in C^{k}\left( \overline{\Omega};\mathbb{R}^n\right)$ satisfying \[ \left\{ \begin{array} [c]{cl} \det\nabla u\left( x\right) =f\left( x\right) \smallskip & x\in \Omega
u\left( x\right) =x & x\in\partial\Omega \end{array} \right. \] where $k\ge 1$ is an integer, $\Omega$ is a bounded smooth domain and $f\in C^{k}\left( \overline{\Omega}\right) $ satisfies \[ \int_{\Omega}f(x) dx=\textrm{meas}\,\Omega \] with no sign hypothesis on $f$.
Download: