Regularity of stable solutions of $p$-Laplace equations through geometric Sobolev type inequalities
Regularity of stable solutions of $p$-Laplace equations through geometric Sobolev type inequalities
We prove a Sobolev and a Morrey type inequality involving the mean curvature and the tangential gradient with respect to the level sets of the function that appears in the inequalities. Then, as an application, we establish a priori estimates for semistable solutions of –\Delta_p u= g(u) in a smooth …