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

We study existence and regularity of solutions to the Dirichlet problem for the prescribed Jacobian equation, [Formula: see text] , where f is integrable and bounded away from zero. In particular, we take [Formula: see text] , where [Formula: see text] , or in [Formula: see text] . We prove that for...

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Detalles Bibliográficos
Autores principales: Guerra, André, Koch, Lukas, Lindberg, Sauli
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7880952/
https://www.ncbi.nlm.nih.gov/pubmed/33612983
http://dx.doi.org/10.1007/s00526-021-01931-9
Descripción
Sumario:We study existence and regularity of solutions to the Dirichlet problem for the prescribed Jacobian equation, [Formula: see text] , where f is integrable and bounded away from zero. In particular, we take [Formula: see text] , where [Formula: see text] , or in [Formula: see text] . We prove that for a Baire-generic f in either space there are no solutions with the expected regularity.

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