On a Supercritical K-Hessian Inequality of Trudinger–Moser Type and Extremal Functions

We establish a supercritical Trudinger–Moser type inequality for the k-Hessian operator on the space of the k-admissible radially symmetric functions Φ<inf>0,rad</inf>k(B), where B is the unit ball in RN. We also prove the existence of extremal functions for this new supercritical inequality. © Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2024.