Phragmén–Lindelöf type theorem for m-hessian equations

Abstract

We derive an interior estimate for the gradient of a solution u to the m-Hessian equation with a certain right-hand side. The estimate depends on the oscillation of u and properties of the right-hand side of the equation. The proof is based on a modification of some ideas of Trudinger (1997). As a consequence of the main result, a theorem of Fragmen–Lindelof type is obtained for solutions to the m-Hessian equations in the entire space $$ \mathbb{R}^n $$ . Bibliography: 4 titles.