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

André Guerra, Lukas Koch*, Sauli Lindberg

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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∈ Lp, where p> 1 , or in Llog L. We prove that for a Baire-generic f in either space there are no solutions with the expected regularity.

Original languageEnglish
Article number55
JournalCalculus of Variations and Partial Differential Equations
Volume60
Issue number1
DOIs
Publication statusPublished - Feb 2021
MoE publication typeA1 Journal article-refereed

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