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

**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.

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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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