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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The $ P$-Laplace equation on a class of Grushin-type spaces


Authors: Thomas Bieske and Jasun Gong
Journal: Proc. Amer. Math. Soc. 134 (2006), 3585-3594
MSC (2000): Primary 35H20; Secondary 17B70
Published electronically: May 31, 2006
MathSciNet review: 2240671
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Abstract | References | Similar Articles | Additional Information

Abstract: We find the fundamental solution to the $ P$-Laplace equation in Grushin-type spaces. The singularity occurs at the sub-Riemannian points, which naturally corresponds to finding the fundamental solution of a generalized Grushin operator in Euclidean space. We then use this solution to find an infinite harmonic function with specific boundary data and to compute the capacity of annuli centered at the singularity. A solution to the 2-Laplace equation in a wider class of spaces is presented.


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Additional Information

Thomas Bieske
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620
Email: tbieske@math.usf.edu

Jasun Gong
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: jgong@umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08394-8
PII: S 0002-9939(06)08394-8
Keywords: Grushin-type spaces, $P$-Laplacian
Received by editor(s): December 20, 2004
Received by editor(s) in revised form: June 28, 2005
Published electronically: May 31, 2006
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.