Riemann boundary value problem for harmonic functions in Clifford analysis

In this article, we mainly deal with the boundary value problem for harmonic function with values in Clifford algebra: Δ[u](x)=0,x∈Rn∖∂Ω,u+(x)=u−(x)G(x)+g1(x),x∈∂Ω,(Du)+(x)=(Du)−(x)A+g2(x),x∈∂Ω,∥u(∞)∥=0,where ∂Ω is a Liapunov surface in Rn, the Dirac operator D=∑k=1nek∂∂xk, u(x)=∑AeAuA(x) are unknow...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische Nachrichten Vol. 287; no. 8-9; pp. 1001 - 1012
Main Authors: Longfei, Gu, Zhongxiang, Zhang
Format: Journal Article
Language:English
Published: Weinheim Blackwell Publishing Ltd 01.06.2014
Wiley Subscription Services, Inc
Subjects:
30G35
boundary value problem
Boundary value problems
Hölder continuous
Optimization
Universal Clifford algebra
ISSN:0025-584X, 1522-2616
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, we mainly deal with the boundary value problem for harmonic function with values in Clifford algebra: Δ[u](x)=0,x∈Rn∖∂Ω,u+(x)=u−(x)G(x)+g1(x),x∈∂Ω,(Du)+(x)=(Du)−(x)A+g2(x),x∈∂Ω,∥u(∞)∥=0,where ∂Ω is a Liapunov surface in Rn, the Dirac operator D=∑k=1nek∂∂xk, u(x)=∑AeAuA(x) are unknown functions with values in a universal Clifford algebra Cl(Vn,n). Under some assumptions, we show that the boundary value problem is solvable.
Bibliography:istex:43B3D93ECD840938CFB3FE2E7DCED09983B42624
NNSF for Young Scholars of China - No. 11001206
ArticleID:MANA201100302
ark:/67375/WNG-G6XHHZ57-8
National Natural Science Foundation of China - No. 11271175; No. 71271158
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201100302