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

 

Solving the $p$-Laplacian on manifolds


Author: Marc Troyanov
Journal: Proc. Amer. Math. Soc. 128 (2000), 541-545
MSC (1991): Primary 31C15, 31C12, 31C45; Secondary 53C20
Published electronically: July 8, 1999
MathSciNet review: 1622993
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Abstract: We prove in this paper that the equation $\Delta _{p}u+h=0$ on a $p$-hyperbolic manifold $M$ has a solution with $p$-integrable gradient for any bounded measurable function $h : M \to \mathbb R$ with compact support.


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Additional Information

Marc Troyanov
Affiliation: Départment de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
Email: troyanov@math.epfl.ch

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05035-2
PII: S 0002-9939(99)05035-2
Keywords: Differential geometry, potential theory, non linear partial differential equations
Received by editor(s): April 6, 1998
Published electronically: July 8, 1999
Communicated by: Peter Li
Article copyright: © Copyright 1999 American Mathematical Society