Abstract and Applied Analysis

On the $A$-Laplacian

Noureddine Aïssaoui

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2003, Number 13 (2003), 743-755.

Dates
First available in Project Euclid: 28 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1059416442

Digital Object Identifier
doi:10.1155/S1085337503303069

Mathematical Reviews number (MathSciNet)
MR1996921

Zentralblatt MATH identifier
1080.46511

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 31B15

Citation

Aïssaoui, Noureddine. On the $A$-Laplacian. Abstr. Appl. Anal. 2003 (2003), no. 13, 743--755. doi:10.1155/S1085337503303069. https://projecteuclid.org/euclid.aaa/1059416442


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