Local solutions of fully nonlinear weakly hyperbolic differential equations in Sobolev spaces
M. Dreher and M. Reissig
Abstract.
The goal of the present paper is to study fully nonlinear
weakly hyperbolic equations of second order with space- and time degeneracy.
A local existence result in Sobolev spaces under sharp Levi conditions
of C^\infty type is proved. These Levi conditions and the behaviour of the
nonlinearities determine the required smoothness of the data and the loss of
Sobolev regularity
Hokkaido Math. J.
Vol. 27, No. 2
(1998),
337-381.
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