Solving the $p$-Laplacian on manifolds
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- by Marc Troyanov PDF
- Proc. Amer. Math. Soc. 128 (2000), 541-545 Request permission
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.References
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Additional Information
- Marc Troyanov
- Affiliation: Départment de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- MR Author ID: 234039
- Email: troyanov@math.epfl.ch
- Received by editor(s): April 6, 1998
- Published electronically: July 8, 1999
- Communicated by: Peter Li
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 541-545
- MSC (1991): Primary 31C15, 31C12, 31C45; Secondary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-99-05035-2
- MathSciNet review: 1622993