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On the Cauchy problem for an equation of surface theory. (Russian. English summary) Zbl 0565.35020

It is shown that the Cauchy problem for the equation \((1+u^ 2_ y)u_{xy}-u_ xu_ yu_{yy}=0\) with initial conditions on the free curve has as many solutions as some nonlinear functional equation. To each solution there corresponds a unique domain of existence.

MSC:

35G25 Initial value problems for nonlinear higher-order PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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