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- Title
The least gradient problem with Dirichlet and Neumann boundary conditions.
- Authors
Dweik, Samer
- Abstract
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, W 1 , p 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.
- Subjects
NEUMANN boundary conditions; DIRICHLET problem; EXPORT duties; NEUMANN problem
- Publication
Advances in Calculus of Variations, 2025, Vol 18, Issue 1, p151
- ISSN
1864-8258
- Publication type
Academic Journal
- DOI
10.1515/acv-2023-0067