Polynomial growth solutions to higher-order linear elliptic equations and systems

Roger Chen and Jiaping Wang

Vol. 229 (2007), No. 1, 49–61

DOI: 10.2140/pjm.2007.229.49

Abstract

For an equation or system of equations Lu = 0, where L is a uniformly elliptic operator of order 2m and u is a map from ℝⁿ to ℝ^N, we prove that the dimension of the space of polynomial growth solutions of degree at most d is bounded by Cd^2mnN, where C is a constant. If the system is in divergence form, we prove that this dimension is in fact bounded by Cd^mnN.

Keywords

polynomial growth solution, linear elliptic equation, linear elliptic system

Mathematical Subject Classification 2000

Primary: 35J30, 35J45

Milestones

Received: 19 April 2005

Revised: 31 August 2006

Accepted: 5 September 2006

Published: 1 January 2007