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

André Guerra; Lukas Koch; Sauli Lindberg

doi:10.1007/s00526-021-01931-9

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

Analysis of PDEs 2021-02-16 v1 Classical Analysis and ODEs

Authors: 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.

Keywords

dirichlet problem jacobian equation sobolev spaces existence regularity baire generic

Cite

@article{arxiv.2009.03621,
  title  = {The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces},
  author = {André Guerra and Lukas Koch and Sauli Lindberg},
  journal= {arXiv preprint arXiv:2009.03621},
  year   = {2021}
}

Comments

14 pages

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