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

共 50 条

[21] Dynamical boundary problem for Dirichlet-to-Neumann operator with critical Sobolev exponent and Hardy potential
Deng, Yanhua
Tan, Zhong
Xie, Minghong
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2021, 62 (62)
[22] Bounded extremal problems in Hardy spaces for the conjugate Beltrami equation in simply-connected domains
Fischer, Yannick
Leblond, Juliette
Partington, Jonathan R.
Sincich, Eva
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2011, 31 (02) : 264 - 285
[23] The Numerical Solution of the Bitsadze-Samarskii Nonlocal Boundary Value Problems with the Dirichlet-Neumann Condition
Ashyralyev, Allaberen
Ozturk, Elif
ABSTRACT AND APPLIED ANALYSIS, 2012,
[24] Solutions for a Variable Exponent Neumann Boundary Value Problems with Hardy Critical Exponent
Zhi, Guizhen
Zhang, Qihu
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2015, 38 (02) : 571 - 603
[25] Comparison results for nonlinear degenerate Dirichlet and Neumann problems with general growth in the gradient
Tian, Yujuan
Li, Fengquan
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 378 (02) : 749 - 763
[26] Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map
Araujo-Cabarcas, Juan Carlos
Engstrom, Christian
Jarlebring, Elias
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 330 : 177 - 192
[27] Dirichlet and Neumann boundary value problems for bi-polyanalytic functions on the bicylinder
Cui, Yanyan
Wang, Chaojun
AIMS MATHEMATICS, 2025, 10 (03): : 4792 - 4818
[28] Hardy potential versus lower order terms in Dirichlet problems: regularizing effects
Arcoya, David
Boccardo, Lucio
Orsina, Luigi
MATHEMATICS IN ENGINEERING, 2023, 5 (01):
[29] Sobolev meets Besov: Regularity for the Poisson equation with Dirichlet, Neumann and mixed boundary values
Schneider, Cornelia
Szemenyei, Flora O.
ANALYSIS AND APPLICATIONS, 2022, 20 (05) : 989 - 1023
[30] Stability for the inverse potential problem by the local Dirichlet-to-Neumann map for the Schrodinger equation
Fathallah, Ines Kamoun
APPLICABLE ANALYSIS, 2007, 86 (07) : 899 - 914

← 1 2 3 4 5 →