A Classification of Isolated Singularities of Elliptic Monge-Ampere Equations in Dimension Two

作者：Galvez Jose A^*; Jimenez Asun; Mira Pablo

来源：Communications on Pure and Applied Mathematics, 2015, 68(12): 2085-2107.

DOI：10.1002/cpa.21581

Let M-1 denote the space of solutions z(x,y) to an elliptic, real analytic Monge-Ampere equation det(D2z)=phi(x,y,z,Dz)>0 whose graphs have a non-removable isolated singularity at the origin. We prove that M-1 is in one-to-one correspondence with M(2)xZ(2), where M-2 is a suitable subset of the class of regular, real analytic, strictly convex Jordan curves in (2). We also describe the asymptotic behavior of solutions of the Monge-Ampere equation in the C-k-smooth case, and a general existence theorem for isolated singularities of analytic solutions of the more general equation det(D2z+A(x,y,z,Dz))=phi(x,y,z,Dz)>0.

• 出版日期2015-12