ENTIRE SOLUTIONS OF THE GENERALIZED HESSIAN INEQUALITY
Abstract
We study the more general Hessian inequality σk1/k(λ(Di(A(|Du|)Dju)))≥f(u) including the Laplacian, p-Laplacian, mean curvature, k-mean curvature and Hessian operators. We give a nonexistence result and provide a sufficient and necessary condition on the global solvability, which is a generalized Keller–Osserman condition. We also discuss the regularity of solutions.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Bone and Joint Diseases
Publication details
- Journal / source
- Rocky Mountain Journal of Mathematics
- Volume
- 56
- Issue
- 2
- Pages
- 441–456
- Publication date
- 1 April 2026
- Language
- EN