Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 03, pp. 1-9.

Title: On the optimal growth of functions with bounded Laplacian

Authors: Lavi Karp (Ort Braude College, Karmiel, Israel)
         Henrik Shahgholian (Royal Inst. of Technology, Stockholm,  Sweden)

Abstract: 
 Using a compactness argument, we introduce a
 Phragmen Lindelof type  theorem for functions
 with bounded Laplacian. The technique is very useful
 in studying unbounded free boundary problems near the
 infinity point and also in approximating integrable
 harmonic functions by those that decrease rapidly at
 infinity. The method is flexible in the sense
 that it can be applied to any operator which admits
 the standard elliptic estimate.

Submitted October 15, 1999. Published January 1, 2000.
Math Subject Classifications: 35J05, 35J60, 31C45.
Key Words: Optimal growth; bounded Laplacian; linear and 
           semi-linear operators; capacity density condition.