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

0349633 - MÚ 2011 RIV GB eng J - Journal Article
Drábek, P. - Namlyeyeva, Yu. - Nečasová, Šárka
Convergence of variational eigenvalues and eigenfunctions to the Dirichlet problem for the p-Laplacian in domains with fine-grained boundary.
Proceedings of the Royal Society of Edinburgh. A - Mathematics. Roč. 140, č. 3 (2010), s. 573-596. ISSN 0308-2105. E-ISSN 1473-7124
R&D Projects: GA ČR GA201/05/0005; GA MŠMT LC06052
Institutional research plan: CEZ:AV0Z10190503
Keywords : perforated domains * homogenization
Subject RIV: BA - General Mathematics
Impact factor: 0.669, year: 2010
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7782353&fileId=S0308210507001035

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.
Permanent Link: http://hdl.handle.net/11104/0189819