## Osaka Journal of Mathematics

### Second order type-changing equations for a scalar function on a plane

#### Abstract

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.

#### Article information

Source
Osaka J. Math., Volume 49, Number 1 (2012), 101-124.

Dates
First available in Project Euclid: 21 March 2012

https://projecteuclid.org/euclid.ojm/1332337240

Mathematical Reviews number (MathSciNet)
MR2903256

Zentralblatt MATH identifier
1246.35137

Subjects
Primary: 58A15: Exterior differential systems (Cartan theory)
Secondary: 58A17: Pfaffian systems

#### Citation

Noda, Takahiro; Shibuya, Kazuhiro. Second order type-changing equations for a scalar function on a plane. Osaka J. Math. 49 (2012), no. 1, 101--124. https://projecteuclid.org/euclid.ojm/1332337240

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