Differential and Integral Equations

Convexity and asymptotic estimates for large solutions of Hessian equations

A. Colesanti, E. Francini, and P. Salani

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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 $\omega$.

Article information

Source
Differential Integral Equations Volume 13, Number 10-12 (2000), 1459-1472.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061135

Mathematical Reviews number (MathSciNet)
MR1787077

Zentralblatt MATH identifier
0977.35046

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B40: Asymptotic behavior of solutions

Citation

Colesanti, A.; Salani, P.; Francini, E. Convexity and asymptotic estimates for large solutions of Hessian equations. Differential Integral Equations 13 (2000), no. 10-12, 1459--1472. https://projecteuclid.org/euclid.die/1356061135.


Export citation