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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
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