A priori estimates for non-coercive Dirichlet problems with subquadratic gradient terms
We deal with some quasilinear elliptic problems posed in a bounded smooth convex domain Ω⊂RN (N≥3), namely {−Δu=λu+μ(x)|∇u|q+f(x),x∈Ω,u=0,x∈∂Ω, where the data satisfy μ∈L∞(Ω),μ⪈0;f∈Lp(Ω),p>N,f⪈0 and 1<q≤2. We provide sufficient conditions on f,μ (allowing μ to vanish on ∂Ω) that yield the shar...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/707896 |
| Acceso en línea: | http://hdl.handle.net/10486/707896 https://dx.doi.org/10.1016/j.jde.2023.04.012 |
| Access Level: | acceso abierto |
| Palabra clave: | Bernstein method Multiplicity Subquadratic gradient terms Renormalized Solutions Order Elliptic Problems Asymptotic Behavior Subquadratic Gradient Terms Bernstein Method Matemáticas |
| Sumario: | We deal with some quasilinear elliptic problems posed in a bounded smooth convex domain Ω⊂RN (N≥3), namely {−Δu=λu+μ(x)|∇u|q+f(x),x∈Ω,u=0,x∈∂Ω, where the data satisfy μ∈L∞(Ω),μ⪈0;f∈Lp(Ω),p>N,f⪈0 and 1<q≤2. We provide sufficient conditions on f,μ (allowing μ to vanish on ∂Ω) that yield the sharp estimate λ‖u‖L∞(Ω)≤C for any bounded solution u with λ∈(0,λ1), which is the non-coercive regime. The estimate leads to remarkable consequences such as a multiplicity result and a precise asymptotic behavior of the bounded but blowing up solutions as λ→0+ |
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