American Institute of Mathematical Sciences

Advanced
September  2008, 3(3): 633-646. doi: 10.3934/nhm.2008.3.633

On the conjugate of periodic piecewise harmonic functions

Dag Lukkassen 1, , Annette Meidell 2, and  Peter Wall 3,

1. 

Narvik University College, and Norut Narvik, P.O.B. 385 N-8505 Narvik, Norway
2. 

Narvik University College, P.O.B. 385 N-8505 Narvik, Norway
3. 

Department of Mathematics, Luleå University, SE-97187 Luleå, Sweden

Received  March 2007 Published  June 2008

The paper considers the conjugate of periodic functions which are piecewise harmonic. In particular, we consider the harmonic conjugate of the solution of the problem of stationary heat conduction through a periodic network of fibres and matrix of arbitrary shape. A numerical example is also presented.
Keywords: elliptic functions, homogenization.
Mathematics Subject Classification: 35B27, 35J60, 73B2.
Citation: Dag Lukkassen, Annette Meidell, Peter Wall. On the conjugate of periodic piecewise harmonic functions. Networks and Heterogeneous Media, 2008, 3 (3) : 633-646. doi: 10.3934/nhm.2008.3.633
[1]

Yao Xu, Weisheng Niu. Periodic homogenization of elliptic systems with stratified structure. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 2295-2323. doi: 10.3934/dcds.2019097
[2]

Jie Zhao. Convergence rates for elliptic reiterated homogenization problems. Communications on Pure and Applied Analysis, 2013, 12 (6) : 2787-2795. doi: 10.3934/cpaa.2013.12.2787
[3]

Rong Dong, Dongsheng Li, Lihe Wang. Regularity of elliptic systems in divergence form with directional homogenization. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 75-90. doi: 10.3934/dcds.2018004
[4]

Fabio Camilli, Claudio Marchi. On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems. Networks and Heterogeneous Media, 2011, 6 (1) : 61-75. doi: 10.3934/nhm.2011.6.61
[5]

Patrick Henning. Convergence of MsFEM approximations for elliptic, non-periodic homogenization problems. Networks and Heterogeneous Media, 2012, 7 (3) : 503-524. doi: 10.3934/nhm.2012.7.503
[6]

Mamadou Sango. Homogenization of the Neumann problem for a quasilinear elliptic equation in a perforated domain. Networks and Heterogeneous Media, 2010, 5 (2) : 361-384. doi: 10.3934/nhm.2010.5.361
[7]

Francisco Crespo, Sebastián Ferrer. On the extended Euler system and the Jacobi and Weierstrass elliptic functions. Journal of Geometric Mechanics, 2015, 7 (2) : 151-168. doi: 10.3934/jgm.2015.7.151
[8]

Shingo Takeuchi. The basis property of generalized Jacobian elliptic functions. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2675-2692. doi: 10.3934/cpaa.2014.13.2675
[9]

Hugo Beirão da Veiga. Elliptic boundary value problems in spaces of continuous functions. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 43-52. doi: 10.3934/dcdss.2016.9.43
[10]

Ying-Chieh Lin, Tsung-Fang Wu. On the semilinear fractional elliptic equations with singular weight functions. Discrete and Continuous Dynamical Systems - B, 2021, 26 (4) : 2067-2084. doi: 10.3934/dcdsb.2020325
[11]

Li Wang, Qiang Xu, Shulin Zhou. $ L^p $ Neumann problems in homogenization of general elliptic operators. Discrete and Continuous Dynamical Systems, 2020, 40 (8) : 5019-5045. doi: 10.3934/dcds.2020210
[12]

José Carmona, Pedro J. Martínez-Aparicio. Homogenization of singular quasilinear elliptic problems with natural growth in a domain with many small holes. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 15-31. doi: 10.3934/dcds.2017002
[13]

Grégoire Allaire, Yves Capdeboscq, Marjolaine Puel. Homogenization of a one-dimensional spectral problem for a singularly perturbed elliptic operator with Neumann boundary conditions. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 1-31. doi: 10.3934/dcdsb.2012.17.1
[14]

Assyr Abdulle, Yun Bai, Gilles Vilmart. Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Discrete and Continuous Dynamical Systems - S, 2015, 8 (1) : 91-118. doi: 10.3934/dcdss.2015.8.91
[15]

Delia Ionescu-Kruse. Elliptic and hyperelliptic functions describing the particle motion beneath small-amplitude water waves with constant vorticity. Communications on Pure and Applied Analysis, 2012, 11 (4) : 1475-1496. doi: 10.3934/cpaa.2012.11.1475
[16]

Yuanxiao Li, Ming Mei, Kaijun Zhang. Existence of multiple nontrivial solutions for a $p$-Kirchhoff type elliptic problem involving sign-changing weight functions. Discrete and Continuous Dynamical Systems - B, 2016, 21 (3) : 883-908. doi: 10.3934/dcdsb.2016.21.883
[17]

Adam M. Oberman. Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 221-238. doi: 10.3934/dcdsb.2008.10.221
[18]

Thomas Y. Hou, Pengfei Liu. Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4451-4476. doi: 10.3934/dcds.2016.36.4451
[19]

Dominik Hafemeyer, Florian Mannel, Ira Neitzel, Boris Vexler. Finite element error estimates for one-dimensional elliptic optimal control by BV-functions. Mathematical Control and Related Fields, 2020, 10 (2) : 333-363. doi: 10.3934/mcrf.2019041
[20]

Evelyn Herberg, Michael Hinze. Variational discretization of one-dimensional elliptic optimal control problems with BV functions based on the mixed formulation. Mathematical Control and Related Fields, 2022  doi: 10.3934/mcrf.2022013

2021 Impact Factor: 1.41

Tools

Metrics

  • PDF downloads (41)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy