Talk:P-Laplacian

Trivial solution
I observe that the minimizer of the functional $$\int_\Omega |\nabla u|^p$$ on the space $$W^{1,p}_0(\Omega)$$ is actually the function $$u\equiv 0$$. So, either one considers the functional $$\frac{1}{p}\int_\Omega |\nabla u|^p - \int_\Omega fu$$ on the space $$W^{1,p}_0(\Omega)$$, or the functional $$\int_\Omega |\nabla u|^p$$ on the set $$ g + W^{1,p}_0(\Omega)$$. —Preceding unsigned comment added by 134.95.214.81 (talk) 14:35, 1 December 2010 (UTC)
 * That was very embarassing. Thanks for the correction. Ray  Talk 14:40, 1 December 2010 (UTC)