Multiplicity results for the assigned Gauss curvature problem in R2
Analysis of PDEs
2009-12-07 v1
Abstract
To study the problem of the assigned Gauss curvature with conical singularities on Riemanian manifolds, we consider the Liouville equation with a single Dirac measure on the two-dimensional sphere. By a stereographic projection, we reduce the problem to a Liouville equation on the euclidean plane. We prove new multiplicity results for bounded radial solutions, which improve on earlier results of C.-S. Lin and his collaborators. Based on numerical computations, we also present various conjectures on the number of unbounded solutions. Using symmetries, some multiplicity results for non radial solutions are also stated.
Cite
@article{arxiv.0809.3845,
title = {Multiplicity results for the assigned Gauss curvature problem in R2},
author = {Jean Dolbeault and Maria J. Esteban and Gabriella Tarantello},
journal= {arXiv preprint arXiv:0809.3845},
year = {2009}
}
Comments
Nonlinear Analysis TMA (2009) to appear