The Keller-Osserman problem for the k-Hessian operator

Abstract

A delicate problem is to obtain existence of positive solutions to the boundary blow-up elliptic equationis the k-Hessian operator and Ω ⊂ R N is a smooth bounded domain. Our goal is to provide a necessary and sufficient condition on g to ensure existence of at least one explosive k-admissible positive solution. The main tools for proving existence are the comparison principle and the method of sub and supersolutions.

On the two symmetries in the theory of m-Hessian operators

“…The first examples of such pattern are the embedding-type theorems for introduced in the papers [5], [29], [27] Hessian integrals. Discussion on some other inherited from the linear case problems may be found, for instance, in the recent papers [28], [7] and many others.…”