Given is the second order equation,(adsbygoogle = window.adsbygoogle || []).push({});

##X_{uv} = A(u,v)X_{u} + B(u,v)X_{v}## defined on a domain ##(u,v)## in the plane.

##X## is a three dimensional vector and ##A## and ##B## are arbitrary smooth functions.

When does such an equation determine a surface in ##R^3## and what in general can be said about the set of solutions?

Same question for ##X_{uu} = A(u,v)X_{u} + B(u,v)X_{v}##

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# Basic question about certain second order PDE's

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