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The best Sobolev trace constant in a domain with oscillating boundary

✍ Scribed by Julián Fernández Bonder; Rafael Orive; Julio D. Rossi

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
219 KB
Volume
67
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper we study homogenization problems for the best constant for the Sobolev trace embedding W 1, p (Ω ) → L q (∂Ω ) in a bounded smooth domain when the boundary is perturbed by adding an oscillation. We find that there exists a critical size of the amplitude of the oscillations for which the limit problem has a weight on the boundary. For sizes larger than critical the best trace constant goes to zero and for sizes smaller than critical it converges to the best constant in the domain without perturbations.

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✍ G. A. Chechkin; C. D'Apice; U. De Maio 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 335 KB

In this paper we deal with the homogenization problem for the Poisson equation in a singularly perturbed domain with multilevel periodically oscillating boundary. This domain consists of the body, a large number of thin cylinders joining to the body through the thin transmission zone with rapidly os