Attainability of the best Sobolev constant in a ball
نویسندگان
چکیده
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...
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.
متن کاملa swot analysis of the english program of a bilingual school in iran
با توجه به جایگاه زبان انگلیسی به عنوان زبانی بین المللی و با در نظر گرفتن این واقعیت که دولت ها و مسئولان آموزش و پرورش در سراسر جهان در حال حاضر احساس نیاز به ایجاد موقعیتی برای کودکان جهت یاد گیری زبان انگلیسی درسنین پایین در مدارس دو زبانه می کنند، تحقیق حاضر با استفاده از مدل swot (قوت ها، ضعف ها، فرصتها و تهدیدها) سعی در ارزیابی مدرسه ای دو زبانه در ایران را دارد. جهت انجام این تحقیق در م...
15 صفحه اولLooking 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 کاملThe 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2018
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-018-1776-7