On the local solvability of Darboux's equation

Pages: 451 - 456, Issue Special, September 2009

 Abstract        Full Text (115.5K)              

Marcus A. Khuri - Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651, United States (email)

Abstract: We reduce the question of local nonsolvability of the Darboux equation, and hence of the isometric embedding problem for surfaces, to the local nonsolvability of a simple linear equation whose type is explicitly determined by the Gaussian curvature.

Keywords:  Local Solvability, Monge-Ampère Equations, Isometric Embeddings
Mathematics Subject Classification:  Primary: 35M10, 53A05; Secondary: 53B20

Received: July 2008;      Revised: June 2009;      Published: September 2009.