Boundary Problems for Harmonic Functions and Norm Estimates for Inverses of Singular Integrals in Two Dimensions

In this paper, we establish sharp well-posedness results for tangential derivative problems for the Laplacian with data in L p , 1 < p < ∞, on curvilinear polygons. Furthermore, we produce norm estimates/formulas for inverses of singular integral operators relevant for the Dirichlet, Neumann,...

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Vydáno v:Numerical functional analysis and optimization Ročník 26; číslo 7-8; s. 851 - 878
Hlavní autor: Mitrea, Irina
Médium: Journal Article
Jazyk:angličtina
Vydáno: Taylor & Francis Group 01.10.2005
Témata:
Curvilinear polygons
Dirichlet problem
Layer potentials
Neumann problem
Primary 45E05, 47A05
Secondary 35J25, 42B20
Tangential derivative problem
ISSN:0163-0563, 1532-2467
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Shrnutí:In this paper, we establish sharp well-posedness results for tangential derivative problems for the Laplacian with data in L p , 1 < p < ∞, on curvilinear polygons. Furthermore, we produce norm estimates/formulas for inverses of singular integral operators relevant for the Dirichlet, Neumann, tangential derivative, and transmission boundary value problems associated with the Laplacian in a distinguished subclass of Lipschitz domains in two dimensions. Our approach relies on Calderón-Zygmund theory and Mellin transform techniques.
Bibliografie:ObjectType-Article-2
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ISSN:0163-0563
1532-2467
DOI:10.1080/01630560500431076