Nonlinear weighted elliptic problem with degenerate coercivity and L 1 data
| dc.contributor.author | Mohammed, Bouguerra | |
| dc.contributor.author | Rabah, Mecheter: Rapporteur | |
| dc.date.accessioned | 2024-07-10T10:44:38Z | |
| dc.date.available | 2024-07-10T10:44:38Z | |
| dc.date.issued | 2024-06 | |
| dc.description.abstract | In this work, we prove the existence of a weak solution of elliptic problem (P) defined by: (P) ( −div(a(x) |∇u| p−2∇u 1+|u| ) + e(x)|u| p−2u = f in Ω; u = 0 on ∂Ω, with f ∈ L 1 (Ω) and the operator Au = −div(a(x) |∇u| p−2∇u 1+|u| ), 1 < p < ∞ is not coercive on W 1,p 0 (Ω) despite being well-defined between W 1,p 0 (Ω) and its dual W−1,p0 (Ω). Degenerate coercivity implies that as |u| becomes large, 1 1+|u| tends to zero. To solve this issue, we are going to approximate the operator by employing truncations in 1 1+|u| to obtain a coercive differential operator. Next, we will prove some a priori estimates on the sequence of approximate solutions, and we shall finally pass to the limit in the approximate problems to establish the existence of a weak solution for the problem (P). | |
| dc.identifier.uri | https://dspace.univ-msila.dz/handle/123456789/43551 | |
| dc.language.iso | en | |
| dc.publisher | Mohamed Boudiaf University of M'sila | |
| dc.subject | weighted Sobolev spaces | |
| dc.subject | pseudo-monotone | |
| dc.subject | operator nonlinear | |
| dc.subject | elliptic equation | |
| dc.subject | weak solution | |
| dc.title | Nonlinear weighted elliptic problem with degenerate coercivity and L 1 data | |
| dc.type | Thesis |