2000 Convexity and asymptotic estimates for large solutions of Hessian equations
A. Colesanti, E. Francini, P. Salani
Differential Integral Equations 13(10-12): 1459-1472 (2000). DOI: 10.57262/die/1356061135

Abstract

We consider the smallest viscosity solution of the Hessian equation $S_k(D^2u)=f(u)$ in $\omega$, that becomes infinite at the boundary of $\omega\subset\mathbb R^n$; here $S_k(D^2u)$ denotes the $k$-th elementary symmetric function of the eigenvalues of $D^2u$, for $k\in\{1,\dots, n\}$. We prove that if $\omega$ is strictly convex and $f$ satisfies suitable assumptions, then the smallest solution is convex. We also establish asymptotic estimates for the behaviour of such a solution near the boundary of $\omega$.

Citation

Download Citation

A. Colesanti. E. Francini. P. Salani. "Convexity and asymptotic estimates for large solutions of Hessian equations." Differential Integral Equations 13 (10-12) 1459 - 1472, 2000. https://doi.org/10.57262/die/1356061135

Information

Published: 2000
First available in Project Euclid: 21 December 2012

zbMATH: 0977.35046
MathSciNet: MR1787077
Digital Object Identifier: 10.57262/die/1356061135

Subjects:
Primary: 35J60
Secondary: 35B40

Rights: Copyright © 2000 Khayyam Publishing, Inc.

Vol.13 • No. 10-12 • 2000
Back to Top