Title

A nonlinear problem for the Laplace equation with a degenerating Robin condition.

Authors

Musolino, Paolo; Mishuris, Gennady

Abstract

We investigate the behavior of the solutions of a mixed problem for the Laplace equation in a domain Ω. On a part of the boundary ∂Ω, we consider a Neumann condition, whereas in another part, we consider a nonlinear Robin condition, which depends on a positive parameter δ in such a way that for δ = 0 it degenerates into a Neumann condition. For δ small and positive, we prove that the boundary value problem has a solution u(δ,·). We describe what happens to u(δ,·) as δ→0 by means of representation formulas in terms of real analytic maps. Then, we confine ourselves to the linear case, and we compute explicitly the power series expansion of the solution.

Subjects

LAPLACE'S equation; NONLINEAR theories; NEUMANN boundary conditions; MATHEMATICAL mappings; PARAMETERS (Statistics)

Publication

Mathematical Methods in the Applied Sciences, 2018, Vol 41, Issue 13, p5211

ISSN

0170-4214

Publication type

Academic Journal

DOI

10.1002/mma.5072