• Corpus ID: 246016161

# A non-parametric Plateau problem with partial free boundary

@inproceedings{Bellettini2022ANP,
title={A non-parametric Plateau problem with partial free boundary},
author={Giovanni Bellettini and Roberta Marziani and Riccardo Scala},
year={2022}
}
• Published 16 January 2022
• Mathematics
We consider a Plateau problem in codimension 1 in the non-parametric setting. A Dirichlet boundary datum is given only on part of the boundary ∂Ω of a bounded convex domain Ω ⊂ R. Where the Dirichlet datum is not prescribed, we allow a free contact with the horizontal plane. We show existence of a solution, and prove regularity for the corresponding minimal surface. Finally we compare these solutions with the classical minimal surfaces of Meeks and Yau, and show that they are equivalent when…
1 Citations
• Mathematics
ESAIM: Control, Optimisation and Calculus of Variations
• 2022
Given a bounded open set $\Omega \subset \mathbb R^2$, we study the relaxation   of the nonparametric area functional in the strict topology in $BV(\Omega;\mathbb R^2)$, and compute it for

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