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- 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