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arXiv · 2009.03621

The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces

André Guerra·Lukas Koch·Sauli Lindberg
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Abstract

We study existence and regularity of solutions to the Dirichlet problem for the prescribed Jacobian equation, $\det Du = f$, where $f$ is integrable and bounded away from zero. In particular, we take $f\in L^p$, where $p > 1$, or in $L\log L$. We prove that for a Baire-generic $f$ in either space there are no solutions with the expected regularity.

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André Guerra, Lukas Koch, Sauli Lindberg. 2020-09-08. The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces. https://doi.org/10.1007/s00526-021-01931-9

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