Abstract and Applied Analysis
Volume 2003 (2003), Issue 13, Pages 743-755
On the -Laplacian
Département de Mathématiques École Normale Supérieure, Ben Souda, Fès BP 5206, Morocco
Received 25 January 2003
Copyright © 2003 Noureddine Aïssaoui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove, for Orlicz spaces such
that satisfies the condition, the nonresolvability of the -Laplacian equation on , where , if is -parabolic. For a large class of Orlicz spaces including Lebesgue spaces (), we also prove that the same equation, with any bounded measurable function with compact support, has a solution with gradient in
if is -hyperbolic.