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Solving a fully nonlinear first order PDE

given a symmetric matrix of Holder continuous functions $A(x)$ such that $$ \frac{1}{C} |\xi|^2 \leq \langle A(x)\xi,\xi \rangle \leq C |\xi|^2 $$ find a vector field $\Phi$ such that $$ D \Phi(x)^t D …
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