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On Boundary Value Problems for Elliptic Equations in a Singular Domain

Published online by Cambridge University Press:  22 January 2016

Kazunari Hayashida
Kazunari Hayashida*
Affiliation:
Nagoya University
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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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 36 , November 1969 , pp. 99 - 115
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1969

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