On the critical polynomial of functionals related to $p$-area (for $1 < p < \infty$) and $p$-Laplace $(1 < p≤2)$ type operators

Abstract

We consider a class of quasilinear elliptic equations whose principal part includes the $p$-area (for $1 < p < \infty$) and the $p$-Laplace (for $1 < p≤ 2)$ operator. For the critical points of the associated functional, we provide estimates of the corresponding critical polynomial.