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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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
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author Guerra, André
Koch, Lukas
Lindberg, Sauli
author_facet Guerra, André
Koch, Lukas
Lindberg, Sauli
author_sort Guerra, André
collection PubMed
description 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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spelling pubmed-78809522021-02-18 The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces Guerra, André Koch, Lukas Lindberg, Sauli Calc Var Partial Differ Equ Article 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. Springer Berlin Heidelberg 2021-02-12 2021 /pmc/articles/PMC7880952/ /pubmed/33612983 http://dx.doi.org/10.1007/s00526-021-01931-9 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Guerra, André
Koch, Lukas
Lindberg, Sauli
The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces
title The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces
title_full The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces
title_fullStr The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces
title_full_unstemmed The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces
title_short The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces
title_sort dirichlet problem for the jacobian equation in critical and supercritical sobolev spaces
topic Article
url 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
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