Remarks on the comparison principle forquasilinear PDE with no zeroth order terms

Shigeaki Koike; Takahiro Kosugi

doi:10.3934/cpaa.2015.14.133

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2015, Volume 14, Issue 1: 133-142. Doi: 10.3934/cpaa.2015.14.133

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Remarks on the comparison principle for quasilinear PDE with no zeroth order terms

Shigeaki Koike^1, and
Takahiro Kosugi^1,

1.
Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578

Received: December 31, 2013

Revised: March 31, 2014

Published: December 2014

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Abstract

A comparison principle for viscosity solutions of second-order quasilinear elliptic partial dierential equations with no zeroth order terms is shown. A dierent transformation from that of Barles and Busca in [3] is adapted to enable us to deal with slightly more general equations.

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Mathematics Subject Classification: Primary: 49L25; Secondary: 35J70, 35J92.

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