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Published online by Cambridge University Press: 22 January 2016
1. Let Ω be a bounded domain in the plane and denotes its closure and boundary by Ω̅ and ∂Ω, respectively. We shall say that the domain Ω is regular, if every point P ∈ ∂û has an 2-dimensional neighborhood U such that dΩ ∩ U can be mapped in a one-to-one way onto a portion of the tangent line through P by a mapping T which together with its inverse is infinitely differentiable. Let L be an elliptic operator of order 2m defined in Ω̅ and let be a normal set of boundary operators of orders mf <2m. If f is a given function in Ω, the boundary value problem II(L,f,Bj) will be to find a solution u of
satisfying
Bju = 0 on ∂Ω, j = 1, …, m.