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Convergence of variational eigenvalues and eigenfunctions to the Dirichlet problem for the p-Laplacian in domains with fine-grained boundary

Published online by Cambridge University Press:  21 May 2010

Pavel Drábek ,
Yuliya Namlyeyeva  and
Šárka Nečasová
Pavel Drábek
Affiliation:
University of West Bohemia, PO Box 314, 30614 Pilsen, Czech Republic (pdrabek@kma.zcu.cz)
Yuliya Namlyeyeva
Affiliation:
Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences, 74 R. Luxemburg st., Donetsk 83114, Ukraine (namleeva@iamm.ac.donetsk.ua)
Šárka Nečasová
Affiliation:
Mathematical Institute of Academy of Sciences of the Czech Republic, Žitná 25, 11567 Prague 1, Czech Republic (matus@math.cas.cz)
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Abstract

We study the problem of the homogenization of Dirichlet eigenvalue problems for the p-Laplace operator in a sequence of perforated domains with fine-grained boundary. Using the asymptotic expansion method, we derive the homogenized problem for the new equation with an additional term of capacity type. Moreover, we show that a sequence of eigenvalues for the problem in perforated domains converges to the corresponding critical levels of the homogenized problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 3 , June 2010 , pp. 573 - 596
Copyright
Copyright © Royal Society of Edinburgh 2010

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