The least gradient problem with Dirichlet and Neumann boundary conditions
<p dir="ltr">In this paper, we consider the BV least gradient problem with Dirichlet condition on a part Γ⊂∂Ω and Neumann boundary condition on its complementary part ∂Ω\Γ. We will show that in the plane this problem is equivalent to an optimal transport problem with import/export ta...
محفوظ في:
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| منشور في: |
2024
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| _version_ | 1864513540431282176 |
|---|---|
| author | Samer Dweik (22047329) |
| author_facet | Samer Dweik (22047329) |
| author_role | author |
| dc.creator.none.fl_str_mv | Samer Dweik (22047329) |
| dc.date.none.fl_str_mv | 2024-11-20T09:00:00Z |
| dc.identifier.none.fl_str_mv | 10.1515/acv-2023-0067 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/The_least_gradient_problem_with_Dirichlet_and_Neumann_boundary_conditions/30024433 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Mathematical sciences Applied mathematics Mixed least gradient problem 1-Laplacian Import-export optimal transport |
| dc.title.none.fl_str_mv | The least gradient problem with Dirichlet and Neumann boundary conditions |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">In this paper, we consider the BV least gradient problem with Dirichlet condition on a part Γ⊂∂Ω and Neumann boundary condition on its complementary part ∂Ω\Γ. We will show that in the plane this problem is equivalent to an optimal transport problem with import/export taxes on ∂Ω\Γ. Thanks to this equivalence, we will be able to show existence and uniqueness of a solution to this mixed least gradient problem, and we will also prove some Sobolev regularity on this solution. We note that these results generalize those in [S. Dweik, <i>W</i>1,<i>p</i> regularity on the solution of the BV least gradient problem with Dirichlet condition on a part of the boundary, Nonlinear Anal. 223 2022, Article ID 113012], where we studied the pure Dirichlet version of this problem.</p><h2>Other Information</h2><p dir="ltr">Published in: Advances in Calculus of Variations<br>License: <a href="http://creativecommons.org/licenses/by/4.0" target="_blank">http://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1515/acv-2023-0067" target="_blank">https://dx.doi.org/10.1515/acv-2023-0067</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_8adce7ab49d88a338c82c4caf59f3b67 |
| identifier_str_mv | 10.1515/acv-2023-0067 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/30024433 |
| publishDate | 2024 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | The least gradient problem with Dirichlet and Neumann boundary conditionsSamer Dweik (22047329)Mathematical sciencesApplied mathematicsMixed least gradient problem1-LaplacianImport-export optimal transport<p dir="ltr">In this paper, we consider the BV least gradient problem with Dirichlet condition on a part Γ⊂∂Ω and Neumann boundary condition on its complementary part ∂Ω\Γ. We will show that in the plane this problem is equivalent to an optimal transport problem with import/export taxes on ∂Ω\Γ. Thanks to this equivalence, we will be able to show existence and uniqueness of a solution to this mixed least gradient problem, and we will also prove some Sobolev regularity on this solution. We note that these results generalize those in [S. Dweik, <i>W</i>1,<i>p</i> regularity on the solution of the BV least gradient problem with Dirichlet condition on a part of the boundary, Nonlinear Anal. 223 2022, Article ID 113012], where we studied the pure Dirichlet version of this problem.</p><h2>Other Information</h2><p dir="ltr">Published in: Advances in Calculus of Variations<br>License: <a href="http://creativecommons.org/licenses/by/4.0" target="_blank">http://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1515/acv-2023-0067" target="_blank">https://dx.doi.org/10.1515/acv-2023-0067</a></p>2024-11-20T09:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1515/acv-2023-0067https://figshare.com/articles/journal_contribution/The_least_gradient_problem_with_Dirichlet_and_Neumann_boundary_conditions/30024433CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/300244332024-11-20T09:00:00Z |
| spellingShingle | The least gradient problem with Dirichlet and Neumann boundary conditions Samer Dweik (22047329) Mathematical sciences Applied mathematics Mixed least gradient problem 1-Laplacian Import-export optimal transport |
| status_str | publishedVersion |
| title | The least gradient problem with Dirichlet and Neumann boundary conditions |
| title_full | The least gradient problem with Dirichlet and Neumann boundary conditions |
| title_fullStr | The least gradient problem with Dirichlet and Neumann boundary conditions |
| title_full_unstemmed | The least gradient problem with Dirichlet and Neumann boundary conditions |
| title_short | The least gradient problem with Dirichlet and Neumann boundary conditions |
| title_sort | The least gradient problem with Dirichlet and Neumann boundary conditions |
| topic | Mathematical sciences Applied mathematics Mixed least gradient problem 1-Laplacian Import-export optimal transport |