# 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} }

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…

## One Citation

### The relaxed area of $S^1$-valued singular maps in the strict $BV$-convergence

- MathematicsESAIM: 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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