# Problem Statement

Given a domain $$\Omega$$, find $$u$$ such that:
$$$
-\nabla \cdot \left( k(u) \nabla u \right) + \kappa u = 0 \in \Omega,
$$$
and 
$$$
\quad k(u) \nabla u \cdot \hat{n} = \sigma \in \partial \Omega,
$$$
where
$$$
  k(u) \equiv \frac{1}{\sqrt{1 + |\nabla u|^2}} \\
  \kappa=1 \\
  \sigma=0.2
$$$

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# Solution
[](image:266 width:500px)
[image:266 align:left]
    Solution to Laplace-Young equation as defined above.