I wish to gain some understanding of the MVP of nonlinear elliptic equation by geometric intuition. Linear elliptic equation case First of all, I have a very good geometric explain of the MVP of Laplace equation, i.e. MVP of laplace equation $\Delta u=0$ in $\Omega$ , $\forall B(x_0,r)\subset \Omega$ is a Ball, we have following identity: $\frac{1}{\mu(\partial(B))}\int_{\partial B}u(x)dx=u(x_0)$ I need to point out first, this property is not difficult to proof by standard integral by part meth…
