Consider the following question:
how would $(u_x)^2+(u_y)^2$ be controlled? This is basically $|\nabla u|^2$ right? The Laplacian is $u_{xx}+u_{yy}$
Is there an application of the maximum principle hiding somewhere here?
Consider the following question:
how would $(u_x)^2+(u_y)^2$ be controlled? This is basically $|\nabla u|^2$ right? The Laplacian is $u_{xx}+u_{yy}$
Is there an application of the maximum principle hiding somewhere here?