Optimal regularity of stable solutions to nonlinear equations involving the $p$-Laplacian

Xavier Cabre, Pietro Miraglio, Manel Sanchon

We consider the equation $-{\Delta }_{p}u=f(u)$ in a smooth bounded domain of ${\mathbb{R}}^n$, where ${\Delta }_p$ is the $p$-Laplace operator. Explicit examples of unbounded stable energy solution…