Homogenization of oscillating boundaries

Alain Damlamian; Klas Pettersson

doi:10.3934/dcds.2009.23.197

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2009, Volume 23, Issue 1&2: 197-219. Doi: 10.3934/dcds.2009.23.197

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Homogenization of oscillating boundaries

Alain Damlamian^1, and
Klas Pettersson^2,

1.
Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées, CNRS UMR 8050, CMC Avenue du Général De Gaulle, 94010 Créteil
2.
Storgatan 1, 75331 Uppsala

Received: October 31, 2007

Revised: February 29, 2008

Published: April 2009

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Abstract

A variational problem on a sequence of 2-dimensional domains with oscillating boundaries is studied. Using the periodic unfolding method, the homogenized problem is obtained in the limit as the period length approaches zero. Several extensions are also given. In this framework, a result of strong convergence is obtained which is new.

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Mathematics Subject Classification: 35B27, 35J20.

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