Extremal Functions for a Supercritical K-Hessian Inequality of Sobolev-Type

Our main purpose in this paper is to investigate a supercritical Sobolev-type inequality for the k-Hessian operator acting on Φ0,radk(B), the space of radially symmetric k-admissible functions on the unit ball B⊂RN. We also prove both the existence of admissible extremal functions for the associated variational problem and the solvability of a related k-Hessian equation with supercritical growth. © 2021 Elsevier Ltd