Boundary asymptotical behavior of large solutions to Hessian equations

Yong Huang

Vol. 244 (2010), No. 1, 85–98

DOI: 10.2140/pjm.2010.244.85

Abstract

We consider the exact asymptotic behavior of smooth solutions to boundary blow-up problems for the k-Hessian equation on Ω, where ∂Ω is strictly (k−1)-convex. Similar results were obtained by Cîrstea and Trombetti when k = n (the Monge–Ampère equation) and by Bandle and Marcus for a semilinear equation.

Keywords

boundary blow-up problem, Hessian equations

Mathematical Subject Classification 2000

Primary: 35J60

Secondary: 35B40

Milestones

Received: 18 September 2008

Revised: 3 February 2009

Accepted: 20 May 2009

Published: 17 November 2009