# American Institute of Mathematical Sciences

2009, 2009(Special): 451-456. doi: 10.3934/proc.2009.2009.451

## On the local solvability of Darboux's equation

 1 Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651, United States

Received  July 2008 Revised  June 2009 Published  September 2009

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.
Citation: Marcus A. Khuri. On the local solvability of Darboux's equation. Conference Publications, 2009, 2009 (Special) : 451-456. doi: 10.3934/proc.2009.2009.451
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