Necessary and sufficient conditions on global solvability for the <i>p</i>-<i>k</i>-Hessian inequalities

Abstract

Abstract In this paper, we discuss the solvability of the p - k -Hessian inequality $\sigma _{k}^{\frac 1k} ( \lambda ( D_{i} (|Du|^{p-2}$ $ D_{j}u ) ) ) \geq f(u)$ on the entire space $\mathbb {R}^{n}$ and provide a necessary and sufficient condition, which can be regarded as a generalized Keller–Osserman condition. Furthermore, we obtain the optimal regularity of solution.

Topics & Concepts