On the galerkln boundary element method for a mixed non-linear boundary value problem

Abstract

We consider a nonlinear mixed boundary value problem for the Lapla-cian in the plane. Using Green's formula the problem is converted into a system of boundary integral equations. For this nonlinear operator equation the existence and uniqueness is proved under the monotonicity assumption on the nonlinearity. Furthermore, we show that the nonlinear mapping is a-proper and when the nonlinear perturbation is Fréchot-differentiable the linearized operator is a-proper and injective. Then we use weak coercivity of the linearized operator in order to derive quasiop-timality estimates for the Galerkin boundary element solutions.

Keywords:

• Non-linear
• mixed
• boundary element method
• Galerkin
• potential
• monotone
• a-proper

AMS:

• 65N35
• 65R40
• 45L10
• 31A10