Existence of Solutions for Jacobian and Hessian Equations Under Smallness Assumptions

Abstract

We discuss three types of problems. The first one involves Jacobian equations and the two others involve Hessian equations. We proceed by fixed point, obtaining the results under a smallness assumption.

Keywords:

• Hessian equations
• Jacobian equations
• Monge-Ampère equation

Mathematics Subject Classification:

• 35A01
• 35A09

ACKNOWLEDGEMENT

The authors thank G. Csato and O. Kneuss for interesting discussions.

Part of the special issue, “Variational Analysis and Applications.”