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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.
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - Feb 2021|
|MoE publication type||A1 Journal article-refereed|