Electron. J. Diff. Eqns., Vol. 2000(2000), No. 03, pp. 1-9.

On the optimal growth of functions with bounded Laplacian

Lavi Karp & Henrik Shahgholian

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.

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Lavi Karp
Department of Applied Mathematics, Ort Braude College,
P.O. Box 78, Karmiel 21982, Israel.
Department of Mathematics, Technion,
32000 Haifa, Israel.
e-mail: karp@techunix.technion.ac.il
Henrik Shahgholian
Department of Mathematics
Royal Institute of Technology
100 44 Stockholm, Sweden
e-mail: henriks@math.kth.se

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