...continuing the discussion of the stationary Euler equation.
$$ \frac{1}{2} \partial_2 ( (\partial_1 \Phi)^2 - (\partial_2 \Phi)^2 ) - \partial_1 (\partial_1 \Phi \partial_2 \Phi) + \partial_2 e(\Phi)= 0$$$ \partial_2 \Phi > k >0, ~ \Phi \in C^{0,1}$ and bounded.
Transformation: $ x \longmapsto y - (x, \Phi(x))$, bilipschitz.
$v(y) = x_2$
want: $v$ analytic in $y_2$.
...ack, I left my glasses at the front of the lecture hall. I can't see the board so well...
Interesting discussion....ah! there was an omitted derivative and agreement ensues.