Problem Statement

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

Solution

laplaceyoung.png
Solution to Laplace-Young equation as defined above.