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

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2021-02
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en
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Calculus of Variations and Partial Differential Equations, Volume 60, issue 1
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.
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| openaire: EC/H2020/834728/EU//QUAMAP
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Guerra , A , Koch , L & Lindberg , S 2021 , ' The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces ' , Calculus of Variations and Partial Differential Equations , vol. 60 , no. 1 , 55 . https://doi.org/10.1007/s00526-021-01931-9