Phragmén--Lindelöf theorem for infinity harmonic functions

Seppo Granlund; Niko Marola

doi:10.3934/cpaa.2015.14.127

Article Contents

2015, Volume 14, Issue 1: 127-132. Doi: 10.3934/cpaa.2015.14.127

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Phragmén--Lindelöf theorem for infinity harmonic functions

Seppo Granlund^1, and
Niko Marola^1,

1.
University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68, FI-00014 University of Helsinki

Received: October 2013

Revised: January 2014

Published: January 2015

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Abstract

We investigate a version of the Phragmén--Lindelöf theorem for solutions of the equation $\Delta_\infty u=0$ in unbounded convex domains. The method of proof is to consider this infinity harmonic equation as the limit of the $p$-harmonic equation when $p$ tends to $\infty$.

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Mathematics Subject Classification: Primary: 35B40; Secondary: 35J70.

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References

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