Open Access
March 2012 Second order type-changing equations for a scalar function on a plane
Takahiro Noda, Kazuhiro Shibuya
Osaka J. Math. 49(1): 101-124 (March 2012).


In this paper, we consider type-changing equations for one unknown function of two variables by using the theory of differential systems. We give fundamental properties and provide a notion of geometric solutions from a viewpoint of contact geometry of second order. Moreover, we study the structure of associated overdetermined systems and obtain an existence condition of solutions of a special class which are called parabolic solutions of type-changing equations.


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Takahiro Noda. Kazuhiro Shibuya. "Second order type-changing equations for a scalar function on a plane." Osaka J. Math. 49 (1) 101 - 124, March 2012.


Published: March 2012
First available in Project Euclid: 21 March 2012

zbMATH: 1246.35137
MathSciNet: MR2903256

Primary: 58A15
Secondary: 58A17

Rights: Copyright © 2012 Osaka University and Osaka City University, Departments of Mathematics

Vol.49 • No. 1 • March 2012
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