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Analyticity of Dirichlet--Neumann Operators on Hölder and Lipschitz Domains
2005
SIAM Journal on Mathematical Analysis
In this paper we take up the question of analyticity properties of Dirichlet-Neumann operators with respect to boundary deformations. In two separate results, we show that if the deformation is sufficiently small and lies either in the class of C 1+α (any α > 0) or Lipschitz functions, then the Dirichlet-Neumann operator is analytic with respect to this deformation. The proofs of both results utilize the "domain flattening" change of variables recently advocated by Nicholls and Reitich for the
doi:10.1137/s0036141004444810
fatcat:qyjrpz7hxnccbeo34ax5pc346q