Expansions of Dirichlet to Neumann operators under perturbations

Abstract

We obtain an asymptotic expansion of the Dirichlet to Neumann operator (DNO) for the Dirichlet problem on perturbations of the unit disk. We write our result in terms of pseudodifferential operators which themselves have expansions in the perturbation parameter. For a given power of the perturbation parameter, m > 0, and a given order, n < 0, we give an algorithm which allows for the expansion of the symbol of the DNO up to mth power in the perturbation parameter, with error terms belonging to symbols of order n.

Keywords:

• boundary value operators
• Dirichlet to Neumann operator
• boundary value problems
• Dirichlet problem

AMS Subject Classifications::

• 35J67
• 35J25