## Solving the $p$-Laplacian on manifolds

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.

Published in:
Proc. Am. Math. Soc., 128, 2, 541-545
Year:
2000
Keywords:
Note:
1991 Mathematics Subject Classification : Primary 31C15, 31C12, 31C45; Secondary 53C20
Laboratories: