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Fall 2002 Viscosity solutions on Grushin-type planes
Thomas Bieske
Illinois J. Math. 46(3): 893-911 (Fall 2002). DOI: 10.1215/ijm/1258130991

Abstract

This paper examines viscosity solutions to a class of fully nonlinear equations on Grushin-type planes. First, viscosity solutions are defined, using subelliptic second order superjets and subjets. Then, a Grushin maximum principle is proved, and as an application, comparison principles for certain types of nonlinear functions follow. This is accomplished by establishing a natural relationship between Euclidean and subelliptic jets, in order to use the viscosity solution technology of Crandall, Ishii, and Lions (1992). The particular example of infinite harmonic functions on certain Grushin-type planes is examined in further detail.

Citation

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Thomas Bieske. "Viscosity solutions on Grushin-type planes." Illinois J. Math. 46 (3) 893 - 911, Fall 2002. https://doi.org/10.1215/ijm/1258130991

Information

Published: Fall 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1029.35079
MathSciNet: MR1951247
Digital Object Identifier: 10.1215/ijm/1258130991

Subjects:
Primary: 35H20
Secondary: 35B05, 49L25

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

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Vol.46 • No. 3 • Fall 2002
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