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Prescribing Gaussian and Geodesic Curvature on Disks

2018; De Gruyter; Volume: 18; Issue: 3 Linguagem: Inglês

10.1515/ans-2018-2021

ISSN

2169-0375

Autores

Sergio Cruz-Blázquez, David Ruiz,

Tópico(s)

Advanced Mathematical Modeling in Engineering

Resumo

Abstract In this paper, we consider the problem of prescribing the Gaussian and geodesic curvature on a disk and its boundary, respectively, via a conformal change of the metric. This leads us to a Liouville-type equation with a non-linear Neumann boundary condition. We address the question of existence by setting the problem in a variational framework which seems to be completely new in the literature. We are able to find minimizers under symmetry assumptions.

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