Author(s):
Thomas Bieske
Title:
Viscosity solutions on Grushin-type
planes
Journal reference: Illinois J. Math. 46 (2002), 893-911
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.
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