Layer Profiles of Solutions to Elliptic Problems under Parameter-Dependent Boundary Conditions
Jorge García-Melián
Universidad de La Laguna, La Laguna, Tenerife, SpainJulio D. Rossi
Universidad de Buenos Aires, ArgentinaJosé C. Sabina de Lis
Universidad de La Laguna, La Laguna, Tenerife, Spain

Abstract
We consider the unique positive solution to the equation Δ_u_ = ur in Ω, where r > 1 and Ω is a smooth bounded domain of ℝ_N_, under one of the boundary conditions u = λ, ∂u/∂ν = λ, ∂u/∂ν = λ_u_ or ∂u/∂ν = λ_u_ – uq on ∂Ω, q > 1. The main interest is determining the exact layer behavior of this solution near ∂Ω in terms of the parameter λ as λ → ∞. Our analysis is completed with the study of the same type of problems involving the p-Laplacian operator.
Cite this article
Jorge García-Melián, Julio D. Rossi, José C. Sabina de Lis, Layer Profiles of Solutions to Elliptic Problems under Parameter-Dependent Boundary Conditions. Z. Anal. Anwend. 29 (2010), no. 4, pp. 451–467
DOI 10.4171/ZAA/1418