The best Sobolev trace constant in domains with holes for critical or subcritical exponents
نویسندگان
چکیده
منابع مشابه
The Best Constant and Extremals of the Sobolev Embeddings in Domains with Holes: the L∞ Case
Let Ω ⊂ R be a bounded, convex domain. We study the best constant of the Sobolev trace embedding W 1,∞(Ω) ↪→ L∞(∂Ω) for functions that vanish in a subset A ⊂ Ω, which we call the hole. That is, we deal with the minimization problem S A = inf ‖u‖W1,∞(Ω)/‖u‖L∞(∂Ω) for functions that verify u |A= 0. We find that there exists an optimal hole that minimizes the best constant S A among subsets of Ω o...
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ژورنال
عنوان ژورنال: The ANZIAM Journal
سال: 2007
ISSN: 1446-1811,1446-8735
DOI: 10.1017/s1446181100012797