منابع مشابه
Sharp Stability Theorems for the Anisotropic Sobolev and Log-sobolev Inequalities on Functions of Bounded Variation
Combining rearrangement techniques with Gromov’s proof (via optimal mass transportation) of the 1-Sobolev inequality, we prove a sharp quantitative version of the anisotropic Sobolev inequality on BV (R). As a corollary of this result, we also deduce a sharp stability estimate for the anisotropic 1-log-Sobolev inequality.
متن کاملSHARP AFFINE Lp SOBOLEV INEQUALITIES
In this paper we prove a sharp affine Lp Sobolev inequality for functions on R. The new inequality is significantly stronger than (and directly implies) the classical sharp Lp Sobolev inequality of Aubin [A2] and Talenti [T], even though it uses only the vector space structure and standard Lebesgue measure on R. For the new inequality, no inner product, norm, or conformal structure is needed at...
متن کاملSharp Sobolev inequalities involving boundary terms
Let (M, g) be a compact Riemannian manifold of dimension n (n ≥ 3) with smooth boundary. In [LZ], we established some sharp trace inequality on (M, g). In this paper we establish some sharp Sobolev inequalities using the method in [LZ]. For n ≥ 3, it was shown by Aubin [Au1] and Talenti [T] that, for p = 2n/(n − 2), 1 S 1 = inf R n |∇u| 2 R n |u| p 2/p u ∈ L p (R n) \ {0}, ∇u ∈ L 2 (R n) , (0.1...
متن کاملSome general forms of sharp Sobolev inequalities
In this paper, we establish some general forms of sharp Sobolev inequalities on the upper half space or any compact Riemannian manifold with smooth boundary. These forms extend some previous results due to Escobar [11], Li and Zhu [18].
متن کاملModified Log-sobolev Inequalities and Isoperimetry
We find sufficient conditions for a probability measure μ to satisfy an inequality of the type ∫ Rd fF ( f ∫ Rd f 2 dμ ) dμ ≤ C ∫ Rd f2c∗ ( |∇f | |f | ) dμ + B ∫ Rd f dμ, where F is concave and c (a cost function) is convex. We show that under broad assumptions on c and F the above inequality holds if for some δ > 0 and ε > 0 one has ∫ ε 0 Φ ( δc [ tF ( 1t ) Iμ(t) ]) dt <∞, where Iμ is the isop...
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: Proceedings of the American Mathematical Society
سال: 1998
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-98-04406-2