Viscosity solutions on Grushin-type planes

Thomas Bieske

Type: Article

Publication Date: 2002-07-01

Citations: 25

DOI: https://doi.org/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.

Locations

Illinois Journal of Mathematics - View - PDF

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+	Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient	1993	Robert Jensen
+	The tangent space in sub-Riemannian geometry	1996	A. Bellaïche
+	Geometry of balls in nilpotent Lie groups	1994	Ron Karidi
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+	Polar coordinates in Carnot groups	2002	Zoltán M. Balogh Jeremy T. Tyson
+	Remark on Non-Uniform Fundamental and Non Smooth Solutions of Some Classes of Differential Operators with Double Characteristics	1999	Nguyễn Minh Trí