Boundary integral operators and boundary value problems for Laplace's equation

被引：1

作者：

Chang, TongKeun ^{[1
]}

Lewis, John L. ^{[2
]}

机构：

[1] Korea Inst Adv Study, Dept Math, KR-139722 Seoul, South Korea

[2] Univ Kentucky, Dept Math, Lexington, KY 40502 USA

来源：

ARKIV FOR MATEMATIK | 2011年 / 49卷 / 02期

关键词：

LAYER POTENTIALS; DIRICHLET PROBLEM; SPACES;

D O I：

10.1007/s11512-010-0135-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we define boundary single and double layer potentials for Laplace's equation in certain bounded domains with d-Ahlfors regular boundary, considerably more general than Lipschitz domains. We show that these layer potentials are invertible as mappings between certain Besov spaces and thus obtain layer potential solutions to the regularity, Neumann, and Dirichlet problems with boundary data in these spaces.

引用

页码：239 / 276

页数：38

共 50 条

[1] Inverse boundary value problems of the Laplace equation
Wang, Q
Onishi, K
[J]. HYDRAULIC ENGINEERING SOFTWARE VIII, 2000, 7 : 425 - 436
[2] Integral equations related to boundary value problems for the Laplace equation in a plane sector
Vasilev, VB
[J]. DIFFERENTIAL EQUATIONS, 1996, 32 (09) : 1187 - 1193
[3] Integral boundary value problems with causal operators
Zhao, Yian
Song, Guangxing
Sun, Xiaoyan
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (08) : 2768 - 2775
[4] An Approximate Grid Solution of a Nonlocal Boundary Value Problem with Integral Boundary Condition for Laplace's Equation
Dosiyev, Adiguzel A.
Reis, Rifat
[J]. THIRD INTERNATIONAL CONFERENCE ON COMPUTATIONAL MATHEMATICS AND ENGINEERING SCIENCES (CMES2018), 2018, 22
[5] BOUNDARY VALUE PROBLEMS ASSOCIATED WITH THE TENSOR LAPLACE EQUATION
DUFF, GFD
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1953, 5 (02): : 196 - 210
[6] Solving Exterior Boundary Value Problems for the Laplace Equation
M. P. Galanin
D. L. Sorokin
[J]. Differential Equations, 2020, 56 : 890 - 899
[7] Solving Exterior Boundary Value Problems for the Laplace Equation
Galanin, M. P.
Sorokin, D. L.
[J]. DIFFERENTIAL EQUATIONS, 2020, 56 (07) : 890 - 899
[8] BOUNDARY CONTRACTION SOLUTION OF NEUMANN AND MIXED BOUNDARY VALUE PROBLEMS OF LAPLACE EQUATION
KIYONO, T
SHIMASAKI, M
[J]. NUMERISCHE MATHEMATIK, 1971, 16 (05) : 442 - +
[9] Transmission problems for the Laplace and elasticity operators:: Regularity and boundary integral formulation
Nicaise, S
Sändig, AM
[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 1999, 9 (06): : 855 - 898
[10] Mixed boundary value problems for the Laplace-Beltrami equation
Duduchava, R.
Tsaava, M.
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2018, 63 (10) : 1468 - 1496

← 1 2 3 4 5 →