Differential and Integral Equations

Bernstein properties of solutions to some higher-order equations

James A. McCoy

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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

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

First available in Project Euclid: 20 December 2012

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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

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