Interaction of scales for a singularly perturbed degenerating nonlinear Robin problem

Authors Organisations
Type Article
Original languageEnglish
Article number20220159
Number of pages18
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2236
Early online date26 Sept 2022
Publication statusPublished - 14 Nov 2022
Permanent link
Show download statistics
View graph of relations
Citation formats


We study the asymptotic behaviour of solutions of a boundary value problem for the Laplace equation in a perforated domain in Rn, n≥3, with a (nonlinear) Robin boundary condition on the boundary of the small hole. The problem we wish to consider degenerates in three respects: in the limit case, the Robin boundary condition may degenerate into a Neumann boundary condition, the Robin datum may tend to infinity, and the size ϵ of the small hole where we consider the Robin condition collapses to 0. We study how these three singularities interact and affect the asymptotic behaviour as ϵ tends to 0, and we represent the solution and its energy integral in terms of real analytic maps and known functions of the singular perturbation parameters.


  • ARTICLES, Research articles, singularly perturbed boundary value problem, Laplace equation, nonlinear Robin condition, perforated domain, integral equations