We determine the global behavior of every C2-solution to the two-dimensional degenerate Monge–Ampère equation, uxxuyy−uxy2=0, over the finitely punctured plane. With this, we classify every solution in the once or twice punctured plane. Moreover, when we have more than two singularities, if the solution u is not linear in a half-strip, we obtain that the singularities are placed at the vertices of a convex polyhedron P and the graph of u is made by pieces of cones outside of P which are suitably glued along the sides of the polyhedron. Finally, if we look for analytic solutions, then there is at most one singularity and the graph of u is either a cylinder (no singularity) or a cone (one singularity).
|Titolo:||Entire solutions of the degenerate Monge–Ampère equation with a finite number of singularities|
|Data di pubblicazione:||2016|
|Appare nelle tipologie:||1.1 Articolo in rivista|