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Generalizations of a Laplacian-type equation in the Heisenberg group and a class of Grushin-type spaces


Authors: Thomas Bieske and Kristen Childers
Journal: Proc. Amer. Math. Soc. 142 (2014), 989-1003
MSC (2010): Primary 53C17, 35H20; Secondary 22E25, 17B70
DOI: https://doi.org/10.1090/S0002-9939-2013-11928-3
Published electronically: December 12, 2013
MathSciNet review: 3148533
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Abstract: In their 1996 paper, Beals, Gaveau and Greiner found the fundamental solution to a $ 2$-Laplace-type equation in a class of sub-Riemannian spaces. This solution is related to the well-known fundamental solution to the $ \texttt {p}$-Laplace equation in Grushin-type spaces and the Heisenberg group. We extend the $ 2$-Laplace-type equation to a $ \texttt {p}$-Laplace-type equation. We show that the obvious generalization does not have desired properties, but rather, our generalization preserves some natural properties.


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Additional Information

Thomas Bieske
Affiliation: Department of Mathematics & Statistics, University of South Florida, 4204 East Fowler Avenue, CMC342, Tampa, Florida 33620
Email: tbieske@math.usf.edu

Kristen Childers
Affiliation: Department of Mathematics & Statistics, University of South Florida, 4204 East Fowler Avenue, CMC342, Tampa, Florida 33620
Email: childers@usf.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11928-3
Keywords: p-Laplace equation, Heisenberg group, Grushin-type plane
Received by editor(s): April 17, 2012
Published electronically: December 12, 2013
Communicated by: James E. Colliander
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.