Existence and non existence results for the singular Nirenberg problem

@article{Marchis2015ExistenceAN,
  title={Existence and non existence results for the singular Nirenberg problem},
  author={Francesca De Marchis and Rafael L'opez-Soriano},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2015},
  volume={55},
  pages={1-35}
}
  • Francesca De Marchis, Rafael L'opez-Soriano
  • Published 2015
  • Mathematics
  • Calculus of Variations and Partial Differential Equations
  • In this paper we study the problem, posed by Troyanov (Trans AMS 324: 793–821, 1991), of prescribing the Gaussian curvature under a conformal change of the metric on surfaces with conical singularities. Such geometrical problem can be reduced to the solvability of a nonlinear PDE with exponential type non-linearity admitting a variational structure. In particular, we are concerned with the case where the prescribed function K changes sign. When the surface is the standard sphere, namely for the… CONTINUE READING

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