The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (183 KB) | Abstract as PDF | Metadata | Table of Contents | ZAA summary
Volume 29, Issue 4, 2010, pp. 451–467
DOI: 10.4171/ZAA/1418

Published online: 2010-10-02

Layer Profiles of Solutions to Elliptic Problems under Parameter-Dependent Boundary Conditions

Jorge García-Melián[1], Julio D. Rossi[2] and José C. Sabina de Lis[3]

(1) Universidad de La Laguna, La Laguna, Tenerife, Spain
(2) Universidad de Buenos Aires, Argentina
(3) Universidad de La Laguna, La Laguna, Tenerife, Spain

We consider the unique positive solution to the equation Δu = ur in Ω, where r > 1 and Ω is a smooth bounded domain of ℝN, under one of the boundary conditions u = λ, ∂u/∂ν = λ, ∂u/∂ν = λu or ∂u/∂ν = λuuq 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.

Keywords: Dependence on parameters, elliptic equations, boundary layers

García-Melián Jorge, Rossi Julio, Sabina de Lis José: Layer Profiles of Solutions to Elliptic Problems under Parameter-Dependent Boundary Conditions. Z. Anal. Anwend. 29 (2010), 451-467. doi: 10.4171/ZAA/1418