On the local solvability of Darboux's equation

Marcus A. Khuri

doi:10.3934/proc.2009.2009.451

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2009, Volume 2009: 451-456. Doi: 10.3934/proc.2009.2009.451 open access

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On the local solvability of Darboux's equation

Marcus A. Khuri^1,

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

Received: June 30, 2008

Revised: May 31, 2009

Published: August 2009

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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.

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Mathematics Subject Classification: Primary: 35M10, 53A05; Secondary: 53B20.

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