Convexity of solutions to boundary blow-up problems

Petri Juutinen

doi:10.3934/cpaa.2013.12.2267

Article Contents

2013, Volume 12, Issue 5: 2267-2275. Doi: 10.3934/cpaa.2013.12.2267

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Convexity of solutions to boundary blow-up problems

Petri Juutinen^1,

1.
Department of Mathematics and Statistics, P.O.Box 35, FIN-40014 University of Jyväskylä

Received: August 31, 2009

Revised: January 31, 2010

Published: August 2013

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Abstract

We prove convexity of solutions to boundary blow-up problems for the singular infinity Laplacian and the $p$-Laplacian for $p\ge 2$. The proof is based on an extension of the results of Alvarez, Lasry and Lions [2] and on estimates of the boundary blow-up rate.

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Mathematics Subject Classification: 35J60, 35J65, 26B25.

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