Asymptotic behavior of the solutions of a nonlinear Robin problem for the Laplace operator in a domain with a small hole: a functional analytic approach
Massimo Lanza de Cristoforis · Complex Variables and Elliptic Equations · 2007
We consider a bounded open subset of with outward unit normal ν o and with , and we assume that the boundary value problem has a solution . Here Go is a function of to . Then we consider another bounded open subset of with and we consider the boundary value problem for ε > 0 small, where is the outward unit normal to . Under suitable conditions on , , Go , we show that for ε > 0 sufficiently small, such a boundary value problem admits locally around a unique solution u(ε,·). Then we show that (suitable restrictions of) u(ε,·) and the energy integral of u(ε,·) can be continued real analytically in the parameter ε around ε = 0.