Differential and Integral Equations

Bernstein properties of solutions to some higher-order equations

James A. McCoy

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 record some Bernstein properties for entire solutions to higher-order elliptic equations, including certain bi-Laplacian equations, other equations which are second order in the eigenvalues of the Hessian of the solution and some geometrically inspired fourth-order equations. We apply a Bernstein result for second-order elliptic equations on noncompact Riemannian manifolds, whose proof is based on techniques of Yau [20].

Article information

Source
Differential Integral Equations Volume 20, Number 10 (2007), 1153-1166.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039300

Mathematical Reviews number (MathSciNet)
MR2365206

Zentralblatt MATH identifier
1212.35062

Subjects
Primary: 35J40: Boundary value problems for higher-order elliptic equations
Secondary: 31A30: Biharmonic, polyharmonic functions and equations, Poisson's equation 31B30: Biharmonic and polyharmonic equations and functions 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35G20: Nonlinear higher-order equations 35J60: Nonlinear elliptic equations

Citation

McCoy, James A. Bernstein properties of solutions to some higher-order equations. Differential Integral Equations 20 (2007), no. 10, 1153--1166. https://projecteuclid.org/euclid.die/1356039300.


Export citation