On the conjugate of periodic piecewise harmonic functions

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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

Abstract
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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 & Heterogeneous Media, 2008, 3 (3) : 633-646. doi: 10.3934/nhm.2008.3.633

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