A Dirichlet type problem for complex polyharmonic functions

被引：3

作者：

Grzebula, H. ^{[1
]}

Michalik, S. ^{[1
]}

机构：

[1] Cardinal Stefan Wyszynski Univ, Fac Math & Nat Sci, Coll Sci, Woycickiego 1-3, PL-01938 Warsaw, Poland

来源：

ACTA MATHEMATICA HUNGARICA | 2017年 / 153卷 / 01期

关键词：

Dirichlet problem; polyharmonic function; Almansi expansion; Lie ball; 31B30; 32A25; 32A50; 35J40;

D O I：

10.1007/s10474-017-0740-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend holomorphically polyharmonic functions on a real ball to a complex set being the union of rotated balls. We solve a Dirichlet type problem for complex polyharmonic functions with the boundary condition given on the union of rotated spheres.

引用

页码：216 / 229

页数：14

共 50 条

[31] Green function representation in the Dirichlet problem for polyharmonic equations in a ball
Kal'menov, T. Sh.
Koshanov, B. D.
Nemchenko, M. Yu.
DOKLADY MATHEMATICS, 2008, 78 (01) : 528 - 530
[32] Construction of polynomial solutions to the Dirichlet problem for the polyharmonic equation in a ball
Karachik, V. V.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2014, 54 (07) : 1122 - 1143
[33] Polyharmonic dirichlet problems
H. Begehr
T. N. H. Vu
Z. -X. Zhang
Proceedings of the Steklov Institute of Mathematics, 2006, 255 (1) : 13 - 34
[34] Weighted integrals for polyharmonic type functions
Stevic, S
HOUSTON JOURNAL OF MATHEMATICS, 2004, 30 (02): : 511 - 521
[35] Representation of the Green's Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball
Karachik, V. V.
DIFFERENTIAL EQUATIONS, 2023, 59 (08) : 1061 - 1074
[36] On solutions of the mixed Dirichlet–Navier problem for the polyharmonic equation in exterior domains
O. A. Matevosyan
Russian Journal of Mathematical Physics, 2016, 23 : 135 - 138
[37] On a new method for constructing the Green function of the Dirichlet problem for the polyharmonic equation
Kal'menov, T. Sh.
Suragan, D.
DIFFERENTIAL EQUATIONS, 2012, 48 (03) : 441 - 445
[38] On a new method for constructing the Green function of the Dirichlet problem for the polyharmonic equation
T. Sh. Kal’menov
D. Suragan
Differential Equations, 2012, 48 : 441 - 445
[39] Representation for the Green's function of the Dirichlet problem for polyharmonic equations in a ball
Kal'menov, T. Sh.
Koshanov, B. D.
SIBERIAN MATHEMATICAL JOURNAL, 2008, 49 (03) : 423 - 428
[40] Representation of the Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball
V. V. Karachik
Differential Equations, 2023, 59 : 1061 - 1074

← 1 2 3 4 5 →