On Neumann and Poincare problems for Laplace equation

被引：0
|
作者：
Vladimir Ryazanov
机构：
[1] National Academy of Sciences of Ukraine,Institute of Applied Mathematics and Mechanics
来源：
Analysis and Mathematical Physics | 2017年 / 7卷
关键词：
Neumann and Poincare problems; Laplace equation; Harmonic functions; Directional derivatives; Nontangential limits; Primary 31A05; 31A20; 31A25; 31B25; 35Q15; Secondary 30E25; 31C05; 34M50; 35F45;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
It is proved the existence of nonclassical solutions of the Neumann problem for the harmonic functions in the Jordan rectifiable domains with arbitrary measurable boundary distributions of normal derivatives. The same is stated for a special case of the Poincare problem on directional derivatives. Moreover, it is shown that the spaces of the found solutions have the infinite dimension.
引用
收藏
页码：285 / 289
页数：4
相关论文
共 50 条
  • [31] On the spectrum of the Neumann problem for Laplace equation in a domain with a narrow slit
    Gadyl'shin, Rustem R.
    Il'in, Arlen M.
    ASYMPTOTIC ANALYSIS, 2010, 67 (3-4) : 167 - 189
  • [32] On a generalization of the Neumann problem for the Laplace equation outside cuts in a plane
    Krutitskii, PA
    Chikilev, AO
    Krutitskaya, NC
    Kolybasova, VV
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2005, 28 (05) : 593 - 606
  • [33] PERFORATED SCREENS PROBLEMS FOR LAPLACE EQUATION
    NGUETSENG, G
    ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 1985, 19 (01): : 33 - 63
  • [34] Numerical solution of a hypersingular integral equation in the Neumann problem for the Laplace equation on a sphere and a torus
    Anfinogenov, AY
    Lifanov, IK
    Lifanov, PI
    DOKLADY MATHEMATICS, 2001, 63 (03) : 322 - 326
  • [35] Essential norms of the integral operator corresponding to the Neumann problem for the Laplace equation
    Medková, D
    Král, J
    MATHEMATICAL ASPECTS OF BOUNDARY ELEMENT METHODS: DEDICATED TO VLADIMIR MAZ'YA ON THE OCCASION OF HIS 60TH BIRTHDAY, 2000, 414 : 215 - 226
  • [36] Shape differentiability of the Neumann problem of the Laplace equation in the half-space
    Amrouche, Cherif
    Necasova, Sarka
    Sokolowski, Jan
    CONTROL AND CYBERNETICS, 2008, 37 (04): : 747 - 769
  • [37] Fundamental Solutions of the 2D Neumann Problem for the Laplace Equation
    A. V. Setukha
    Differential Equations, 2003, 39 : 135 - 144
  • [38] Neumann problem in divergence form modeled on the p(x)-Laplace equation
    El Amrouss, Abdelrachid
    Moradi, Fouzia
    Ourraoui, Anass
    BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2014, 32 (02): : 109 - 117
  • [39] On the discretization of Laplace's equation with Neumann boundary conditions on polygonal domains
    Hoskins J.
    Rachh M.
    Journal of Computational Physics: X, 2020, 8
  • [40] Fundamental solutions of the 2D Neumann problem for the Laplace equation
    Setukha, AV
    DIFFERENTIAL EQUATIONS, 2003, 39 (01) : 135 - 144
12345