On the conjugate of periodic piecewise harmonic functions

Dag Lukkassen; Annette Meidell; Peter Wall

doi:10.3934/nhm.2008.3.633

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2008, Volume 3, Issue 3: 633-646. Doi: 10.3934/nhm.2008.3.633

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On the conjugate of periodic piecewise harmonic functions

1.
Narvik University College, and Norut Narvik, P.O.B. 385 N-8505 Narvik
2.
Narvik University College, P.O.B. 385 N-8505 Narvik
3.
Department of Mathematics, Luleå University, SE-97187 Luleå

Received: February 28, 2007

Published: August 2008

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Abstract

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:

homogenization,
elliptic functions.

Mathematics Subject Classification: 35B27, 35J60, 73B27.

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