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Solving the -Laplacian on manifolds

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

References:

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3.: E. Hebey, Sobolev spaces on Riemannian manifolds, Springer Lect. Notes in Math. 1635. CMP 98:04
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6.: M. Troyanov, Parabolicity of manifolds, préprint EPFL, 1997.


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