A characterization of semistable radial solutions of k-Hessian equations

Abstract

We characterize semistable radial solutions of the equationSk(D2u)=g(u)in B1, where B1 is the unit ball of Rn, D2u is the Hessian matrix of u,g is a positive C1 nonlinearity and Sk(D2u) denotes the k-Hessian operator of u. This class of radial solutions has been recently introduced by the authors. The proofs are new focusing on the structure of the equation directly, thereby improving some previous results.