منابع مشابه
Best Constant in Sobolev Inequality
The equality sign holds in (1) i] u has the Jorm: (3) u(x) = [a + btxI,~',-'] 1-~1~ , where Ix[ = (x~ @ ...-~x~) 1⁄2 and a, b are positive constants. Sobolev inequalities, also called Sobolev imbedding theorems, are very popular among writers in part ial differential equations or in the calculus of variations, and have been investigated by a great number of authors. Nevertheless there is a ques...
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We prove that the best constant in the Sobolev inequality (WI,” c Lp* with $= f i and 1 c p < n) is achieved on compact Riemannian manifolds, or only complete under some hypotheses. We also establish stronger inequalities where the norms are to some exponent which seems optimal. 0 Elsevier, Paris
متن کاملLooking for the Best Constant in a Sobolev Inequality: A Numerical Approach
A numerical method for the computation of the best constant in a Sobolev inequality involving the spacesH2(Ω) and C0(Ω) is presented. Green’s functions corresponding to the solution of Poisson problems are used to express the solution. This (kind of) non-smooth eigenvalue problem is then formulated as a constrained optimization problem and solved with two different strategies: an augmented Lagr...
متن کاملSymmetrization of Functions and the Best Constant of 1-DIM Lp Sobolev Inequality
1 Department of Computer Science, National Defense Academy, 1-10-20 Hashirimizu, Yokosuka 239-8686, Japan 2 Graduate School of Mathematical Sciences, Faculty of Engineering Science, Osaka University, 1–3 Matikaneyamatyo, Toyonaka 560-8531, Japan 3 Liberal Arts and Basic Sciences, College of Industrial Technology, Nihon University, 2-11-1 Shinei, Narashino 275-8576, Japan 4 Department of Monozuk...
متن کاملThe 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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ژورنال
عنوان ژورنال: Annali di Matematica Pura ed Applicata
سال: 1976
ISSN: 0373-3114,1618-1891
DOI: 10.1007/bf02418013