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

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.

arXiv comment14 pages

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Cited by in corpus (1)

• Energy minimisers with prescribed Jacobian