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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Bibliographic Details
Published in:	Numerical functional analysis and optimization Vol. 26; no. 7-8; pp. 851 - 878
Main Author:	Mitrea, Irina
Format:	Journal Article
Language:	English
Published:	Taylor & Francis Group 01.10.2005
Subjects:	Curvilinear polygons Dirichlet problem Layer potentials Neumann problem Primary 45E05, 47A05 Secondary 35J25, 42B20 Tangential derivative problem
ISSN:	0163-0563, 1532-2467
Online Access:	Get full text
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Summary:	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.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0163-0563 1532-2467
DOI:	10.1080/01630560500431076