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Periodic Riemannian manifold with preassigned gaps in spectrum of Laplace–Beltrami operator

✍ Scribed by Andrii Khrabustovskyi

Book ID
113699283
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
398 KB
Volume
252
Category
Article
ISSN
0022-0396

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Homogenization of eigenvalue problem for
Homogenization of eigenvalue problem for Laplace–Beltrami operator on Riemannian manifold with complicated ‘bubble-like’ microstructure
✍ Andrii Khrabustovskyi 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 151 KB

## Abstract We study the asymptotic behavior of the eigenvalues and the eigenfunctions of the Laplace–Beltrami operator on a Riemannian manifold __M__^ε^ depending on a small parameter ε>0 and whose structure becomes complicated as ε→0. Under a few assumptions on scales of __M__^ε^ we obtain the ho