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).

引用

页码：504 / 538

页数：35

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