# differential equations – Solving a completely nonlinear first bid PDE retort

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## differential equations – Solving a completely nonlinear first bid PDE

given a symmetric matrix of Holder steady features $$A(x)$$ such that
$$frac{1}{C} |xi|^2 leq langle A(x)xi,xi rangle leq C |xi|^2$$

discover a vector bailiwick $$Phi$$ such that
$$D Phi(x)^t D Phi (x) = A(x)^tA(x)$$

as a simplified model of the issue, if somebody may support me with the next totally nonlinear first bid PDE

given a Holder steady obligation $$a(x)>lambda >0$$, discover a obligation $$Psi$$ such that
$$|nabla Psi(x)|^2= |a(x)|^2$$

assassinate any of the above issues maintain an answer?

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