A characterization of semistable radial solutions of k-Hessian equations

2020/05/13 by Navarro, Miguel Angel, Sánchez, Justino
#35B07 (secondary) #35B35 #35J25 (primary) #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.06348

Abstract

We characterize semistable radial solutions of the equation S_k(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 S_k(D²u) denotes the k-Hessian operator of u. This class of radial solutions has been recently introduced by the authors in [8]. The proofs are new relative to those given in [8] and focus on the structure of the equation directly, thereby improving some previous results.

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