Prescribing Gaussian and Geodesic Curvature on Disks-Reference-Cited by-同舟云学术

Prescribing Gaussian and Geodesic Curvature on Disks

Published:2018-07-20 Issue:3 Volume:18 Page:453-468
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Cruz-Blázquez Sergio¹,Ruiz David²

Affiliation:

1. Scuola Normale Superiore , Piazza dei Cavalieri 7, 56126 Pisa , Italy

2. Departamento de Análisis Matemático , Universidad de Granada , Campus Fuentenueva, 18071 Granada , Spain

Abstract

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.

Funder

Ministerio de Economía, Industria y Competitividad

Junta de Andalucía

Marie Skłodowska-Curie Actions

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2018-2021/pdf

Reference33 articles.

1. A. Ambrosetti, Y. Li and A. Malchiodi, On the Yamabe problem and the scalar curvature problems under boundary conditions, Math. Ann. 322 (2002), no. 4, 667–699. 10.1007/s002080100267