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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503303069 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832555843162210304 |
|---|---|
| author | Noureddine Aïssaoui |
| author_facet | Noureddine Aïssaoui |
| author_sort | Noureddine Aïssaoui |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-1678c746b03f49daa7352b1cfd256443 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1678c746b03f49daa7352b1cfd2564432025-02-03T05:46:57ZengWileyAbstract 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 |
| spellingShingle | Noureddine Aïssaoui On the A-Laplacian Abstract and Applied Analysis |
| title | On the A-Laplacian |
| title_full | On the A-Laplacian |
| title_fullStr | On the A-Laplacian |
| title_full_unstemmed | On the A-Laplacian |
| title_short | On the A-Laplacian |
| title_sort | on the a laplacian |
| url | http://dx.doi.org/10.1155/S1085337503303069 |
| work_keys_str_mv | AT noureddineaissaoui onthealaplacian |