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A comparison theorem for the Levi equation. (English) Zbl 0822.35009
Summary: We prove a strong comparison principle for the solution of the Levi equation \[ \begin{split} \sum_{i=1}^ n \bigl( (1+u^ 2_ t) (u_{x_ i x_ i}+ u_{y_ i y_ i})+ (u^ 2_{x_ i}+ u^ 2_{y_ i}) u_{tt}+ 2(u_{y_ i} -u_{x_ i} u_ t) u_{x_ j t}- 2(u_{x_ i}+ u_{y_ i} u_ t) u_{y_ i t} \bigr)+\\ +k(x,y,t) (1+| Du|^ 2 )^{3/2} =0, \end{split} \] applying the Bony propagation principle.

MSC:
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35G20 Nonlinear higher-order PDEs
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