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.
|Titolo:||Blow-up techniques and regularity near the boundary for free discontinuity problems|
|Data di pubblicazione:||2001|
|Digital Object Identifier (DOI):||10.1515/ans-2001-0201|
|Appare nelle tipologie:||1.1 Articolo in rivista|