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).

Entire solutions of the degenerate Monge–Ampère equation with a finite number of singularities

NELLI, BARBARA
2016

Abstract

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).
File in questo prodotto:
File Dimensione Formato  
GalvezNelli-JDE.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Dominio pubblico
Dimensione 1.12 MB
Formato Adobe PDF
1.12 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/107963
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact