Sharp constant for a 2D anisotropic Sobolev inequality with critical nonlinearity
نویسندگان
چکیده
منابع مشابه
A fully anisotropic Sobolev inequality
Let n ≥ 2 and let A : Rn → [0,∞] be any convex function satisfying the following properties: A(0) = 0 and A(ξ) = A(−ξ) for ξ ∈ R; (1.1) for every t > 0, {ξ ∈ R : A(ξ) ≤ t} (1.2) is a compact set whose interior contains 0. Observe that A need not depend on the length |ξ| of ξ nor be the sum of functions of its components ξi, i = 1, . . . , n. The purpose of this note is to exhibit an inequality ...
متن کاملDouble Logarithmic Inequality with a Sharp Constant
We prove a Log Log inequality with a sharp constant. We also show that the constant in the Log estimate is “almost” sharp. These estimates are applied to prove a Moser-Trudinger type inequality for solutions of a 2D wave equation.
متن کاملDouble Logarithmic Inequality with a Sharp Constant
We prove a Log Log inequality with a sharp constant. We also show that the constant in the Log estimate is “almost” sharp. These estimates are applied to prove a Moser-Trudinger type inequality for solutions of a 2D wave equation.
متن کاملA sharp Sobolev inequality on Riemannian manifolds
Let (M, g) be a smooth compact Riemannian manifold without boundary of dimension n ≥ 6. We prove that ‖u‖ L2 ∗ (M,g) ≤ K 2 ∫ M { |∇gu| 2 + c(n)Rgu 2 } dvg + A‖u‖ 2 L2n/(n+2)(M,g), for all u ∈ H(M), where 2 = 2n/(n − 2), c(n) = (n − 2)/[4(n − 1)], Rg is the scalar curvature, K −1 = inf ‖∇u‖L2(Rn)‖u‖ −1 L2n/(n−2)(Rn) and A > 0 is a constant depending on (M, g) only. The inequality is sharp in the...
متن کاملBest 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 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: Journal of Mathematical Analysis and Applications
سال: 2010
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2010.02.020