THE BEST SOBOLEV TRACE CONSTANT IN PERIODIC MEDIA FOR CRITICAL AND SUBCRITICAL EXPONENTS
نویسندگان
چکیده
منابع مشابه
The Best Sobolev Trace Constant as Limit of the Usual Sobolev Constant for Small Strips near the Boundary
In this paper we prove that the best constant in the Sobolev trace embedding H(Ω) ↪→ L(∂Ω) in a bounded smooth domain can be obtained as the limit as ε → 0 of the best constant of the usual Sobolev embedding H(Ω) ↪→ L(ωε, dx/ε) where ωε = {x ∈ Ω : dist(x, ∂Ω) < ε} is a small neighborhood of the boundary. We also analyze symmetry properties of extremals of this last embedding when Ω is a ball.
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Let Ω ⊂ RN be a bounded, smooth domain. We deal with the best constant of the Sobolev trace embedding W 1,p(Ω) ↪→ Lq(∂Ω) for functions that vanish in a subset 17 A ⊂ Ω, which we call the hole, i.e. we deal with the minimization problem SA = inf ‖u‖ W1,p(Ω) /‖u‖ Lq(∂Ω) for functions that verify u |A = 0. It is known that there 19 exists an optimal hole that minimizes the best constant SA among s...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2009
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089509990048