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2005 A weak maximum principle for the linearized operator of $m$-Laplace equations with applications to a nondegeneracy result
Berardino Sciunzi
Adv. Differential Equations 10(2): 223-240 (2005).

Abstract

We consider the Dirichlet problem for positive solutions of the equation $ -\Delta_m (u) = f(u) \; $ in a bounded, smooth domain $\, \Omega $, with $f$ positive and locally Lipschitz continuous. We prove a weak maximum principle in small domains for the linearized operator that we exploit to prove a weak maximum principle for the linearized operator. We then consider the case $f(s)=s^q$ and prove a nondegeneracy result in weighted Sobolev spaces.

Citation

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Berardino Sciunzi. "A weak maximum principle for the linearized operator of $m$-Laplace equations with applications to a nondegeneracy result." Adv. Differential Equations 10 (2) 223 - 240, 2005.

Information

Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1122.35020
MathSciNet: MR2106131

Subjects:
Primary: 35J60
Secondary: 35B05, 35B50

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.10 • No. 2 • 2005
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