Large solutions to an anisotropic quasilinear elliptic problem
In this paper we consider existence, asymptotic behavior near the boundary and uniqueness of positive solutions to the problem: divx(|∇xu| p−2∇xu)(x, y) + divy(|∇yu| q−2∇yu)(x, y) = u r (x, y) in a bounded domain Ω⊂RN×RMΩ⊂RN×RM together with the boundary condition u (x, y) = ∞ on ∂Ω. We prove that t...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2010 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/16520 |
| Acceso en línea: | http://hdl.handle.net/11336/16520 |
| Access Level: | acceso abierto |
| Palabra clave: | Anisotripic problems https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In this paper we consider existence, asymptotic behavior near the boundary and uniqueness of positive solutions to the problem: divx(|∇xu| p−2∇xu)(x, y) + divy(|∇yu| q−2∇yu)(x, y) = u r (x, y) in a bounded domain Ω⊂RN×RMΩ⊂RN×RM together with the boundary condition u (x, y) = ∞ on ∂Ω. We prove that the necessary and sufficient condition for the existence of a solution u∈W1,p,qloc(Ω)u∈Wloc1,p,q(Ω) to this problem is r > max{p−1, q−1}. Assuming that r > q−1 ≥ p−1 > 0 we will show that the exponent q controls the blow-up rates near the boundary in the sense that all points of ∂Ω share the same profile, that depends on q and r but not on p, with the sole exception of the vertical points (where the exponent p plays a role). |
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