Dirichlet/Neumann problems and Hardy classes for the planar conductivity equation

被引：11
|
作者：
Baratchart, Laurent [1 ]
Fischer, Yannick [2 ]
Leblond, Juliette [1 ]
机构：
[1] INRIA Sophia Antipolis, Team APICS, F-06902 Sophia Antipolis, France
[2] Univ Nice Sophia Antipolis, Lab Math JA Dieudonne, UMR CNRS UNSA 7351, F-06108 Nice 02, France
来源：
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2014年 / 59卷 / 04期
关键词：
Hardy spaces; boundary value problems; second-order ellipticequations; conjugate functions; integral equations with kernels of Cauchy type; 30C62; 30E25; 30H10; 34K29; 35J56; ELLIPTIC-EQUATIONS; INVERSE PROBLEMS; APPROXIMATION; SPACES; SUBSETS;
D O I：
10.1080/17476933.2012.755755
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study Hardy spaces H (p)(v) of the conjugate Beltrami equation partial derivative f = v partial derivative f over Dini-smooth finitely connected domains, for real contractive v is an element of W-1,W-r with r > 2, in the range 1 < p < infinity. We develop a theory of conjugate functions and apply it to solve Dirichlet and Neumann problems for the conductivity equation. del(center dot) ( sigma del u) = 0 where sigma = ( 1 - v)/( 1 + v).
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页码：504 / 538
页数：35
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