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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Veröffentlicht in:Numerical functional analysis and optimization Jg. 26; H. 7-8; S. 851 - 878
1. Verfasser: Mitrea, Irina
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Taylor & Francis Group 01.10.2005
Schlagworte:
Curvilinear polygons
Dirichlet problem
Layer potentials
Neumann problem
Primary 45E05, 47A05
Secondary 35J25, 42B20
Tangential derivative problem
ISSN:0163-0563, 1532-2467
Online-Zugang:Volltext
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0163-0563
1532-2467
DOI:10.1080/01630560500431076