On the A-Laplacian
We prove, for Orlicz spaces LA(ℝN) such that A satisfies the Δ2 condition, the nonresolvability of the A-Laplacian equation ΔAu+h=0 on ℝN, where ∫h≠0, if ℝN 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 bounde...
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Hindawi Limited
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503303069 |
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doaj-1678c746b03f49daa7352b1cfd2564432020-11-24T22:07:27ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092003-01-0120031374375510.1155/S1085337503303069On the A-LaplacianNoureddine Aïssaoui0Département de Mathématiques École Normale Supérieure, Ben Souda, Fès BP 5206, MoroccoWe prove, for Orlicz spaces LA(ℝN) such that A satisfies the Δ2 condition, the nonresolvability of the A-Laplacian equation ΔAu+h=0 on ℝN, where ∫h≠0, if ℝN 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(ℝN) if ℝN is A-hyperbolic.http://dx.doi.org/10.1155/S1085337503303069 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Noureddine Aïssaoui |
| spellingShingle |
Noureddine Aïssaoui On the A-Laplacian Abstract and Applied Analysis |
| author_facet |
Noureddine Aïssaoui |
| author_sort |
Noureddine Aïssaoui |
| title |
On the A-Laplacian |
| title_short |
On the A-Laplacian |
| title_full |
On the A-Laplacian |
| title_fullStr |
On the A-Laplacian |
| title_full_unstemmed |
On the A-Laplacian |
| title_sort |
on the a-laplacian |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2003-01-01 |
| description |
We prove, for Orlicz spaces LA(ℝN) such
that A satisfies the Δ2 condition, the nonresolvability of the A-Laplacian equation ΔAu+h=0 on ℝN, where ∫h≠0, if ℝN 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(ℝN) if ℝN is A-hyperbolic. |
| url |
http://dx.doi.org/10.1155/S1085337503303069 |
| work_keys_str_mv |
AT noureddineaissaoui onthealaplacian |
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1725820309015101440 |