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17 July 2003 On the $A$-Laplacian
Noureddine Aïssaoui
Abstr. Appl. Anal. 2003(13): 743-755 (17 July 2003). DOI: 10.1155/S1085337503303069


We prove, for Orlicz spaces LA(N) such that A satisfies the Δ2 condition, the nonresolvability of the A-Laplacian equation ΔAu+h=0 on N, where h0, if N is A-parabolic. For a large class of Orlicz spaces including Lebesgue spaces Lp (p>1), we also prove that the same equation, with any bounded measurable function h with compact support, has a solution with gradient in LA(N) if N is A-hyperbolic.


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Noureddine Aïssaoui. "On the $A$-Laplacian." Abstr. Appl. Anal. 2003 (13) 743 - 755, 17 July 2003.


Published: 17 July 2003
First available in Project Euclid: 28 July 2003

zbMATH: 1080.46511
MathSciNet: MR1996921
Digital Object Identifier: 10.1155/S1085337503303069

Primary: 31B15 , 46E35

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 13 • 17 July 2003
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