Annales Academię Scientiarum Fennicę
Mathematica
Volumen 37, 2012, 119-134
University of South Florida, Department of Mathematics and Statistics
Tampa, FL 33620, U.S.A.; tbieske 'at' math.usf.edu
Abstract. We prove a sub-Riemannian maximum principle for semicontinuous functions. We apply this principle to Carnot groups to provide a "sub-Riemannian" proof of the uniqueness of viscosity infinite harmonic functions. This is an alternate method of proof from the one found in [15]. We also establish the equivalence of weak solutions and viscosity solutions to the p-Laplace equation. This result extends the author's previous work in the Heisenberg group [3,4].
2010 Mathematics Subject Classification: Primary 53C17, 35D40, 31C45, 35H20; Secondary 31B05, 22E25.
Key words: Sub-Riemannian geometry, non-linear potential theory, viscosity solutions, p-Laplacian.
Reference to this article: T. Bieske: A sub-Riemannian maximum principle and its application to the p-Laplacian in Carnot groups. Ann. Acad. Sci. Fenn. Math. 37 (2012), 119-134.
doi:10.5186/aasfm.2012.3706
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