Differential and Integral Equations
- Differential Integral Equations
- Volume 20, Number 10 (2007), 1153-1166.
Bernstein properties of solutions to some higher-order equations
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 .
Differential Integral Equations Volume 20, Number 10 (2007), 1153-1166.
First available in Project Euclid: 20 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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.