A Riemann jump problem for biharmonic functions in fractal domains

被引：1
|
作者：
Abreu Blaya, Ricardo [1 ]
机构：
[1] Univ Autonoma Guerrero, Fac Matemat, Chilpancingo, Mexico
来源：
ANALYSIS AND MATHEMATICAL PHYSICS | 2021年 / 11卷 / 01期
关键词：
Biharmonic functions; Fractals; Lipschitz classes; Riemann problem; DIRICHLET PROBLEM;
D O I：
10.1007/s13324-020-00469-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Biharmonic functions are the solutions of the fourth order partial differential equation Delta Delta omega = 0. The purpose of this paper is to solve a kind of Riemann boundary value problem for biharmonic functions assuming higher order Lipschitz boundary data. We approach this problem making use of generalized Teodorescu transforms for obtaining the explicit expression of its solution in a Jordan domain Omega subset of R-2 with fractal boundary.
引用
收藏
页数：13
相关论文
共 50 条
  • [41] Bivariate fractal interpolation functions on rectangular domains
    Qian, XY
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2002, 20 (04) : 349 - 362
  • [42] A Hilbert Transform for Matrix Functions on Fractal Domains
    R. Abreu-Blaya
    J. Bory-Reyes
    F. Brackx
    H. De Schepper
    F. Sommen
    Complex Analysis and Operator Theory, 2012, 6 : 359 - 372
  • [43] A Hilbert Transform for Matrix Functions on Fractal Domains
    Abreu-Blaya, R.
    Bory-Reyes, J.
    Brackx, F.
    De Schepper, H.
    Sommen, F.
    COMPLEX ANALYSIS AND OPERATOR THEORY, 2012, 6 (02) : 359 - 372
  • [44] A Cauchy transform for polyanalytic functions on fractal domains
    Gomez Santiesteban, Tania Rosa
    Abreu Blaya, Ricardo
    Bory Reyes, Juan
    Sigarreta Almira, Jose Maria
    ANNALES POLONICI MATHEMATICI, 2018, 121 (01) : 21 - 32
  • [45] BIVARIATE FRACTAL INTERPOLATION FUNCTIONS ON RECTANGULAR DOMAINS
    Xiao-yuan Qian (Department of Applied Mathematics
    Journal of Computational Mathematics, 2002, (04) : 349 - 362
  • [46] A Cauchy Transform for Polymonogenic Functions on Fractal Domains
    Gomez Santiesteban, Tania Rosa
    Abreu Blaya, Ricardo
    Hernandez Gomez, Juan C.
    Sigarreta Almira, Jose Maria
    COMPLEX ANALYSIS AND OPERATOR THEORY, 2022, 16 (03)
  • [47] A Cauchy Transform for Polymonogenic Functions on Fractal Domains
    Tania Rosa Gómez Santiesteban
    Ricardo Abreu Blaya
    Juan C. Hernández Gómez
    José María Sigarreta Almira
    Complex Analysis and Operator Theory, 2022, 16
  • [48] A family of the Riemann problem approximate solutions preserving jump conditions
    Pogorelov, NV
    Semenov, AY
    DOKLADY AKADEMII NAUK, 1997, 352 (02) : 196 - 200
  • [49] Jump problem for differentiable functions with applications
    Katz D.B.
    Kats B.A.
    Lobachevskii Journal of Mathematics, 2017, 38 (3) : 456 - 465
  • [50] Concerning the limit value problem in the theory of biharmonic functions
    Brodsky, GA
    COMPTES RENDUS DE L ACADEMIE DES SCIENCES DE L URSS, 1941, 31 : 208 - 209
12345