An optimal pointwise Morrey-Sobolev inequality
نویسندگان
چکیده
منابع مشابه
Affine Moser-Trudinger and Morrey-Sobolev inequalities
Abstract: An affine Moser-Trudinger inequality, which is stronger than the Euclidean MoserTrudinger inequality, is established. In this new affine analytic inequality an affine energy of the gradient replaces the standard L energy of gradient. The geometric inequality at the core of the affine Moser-Trudinger inequality is a recently established affine isoperimetric inequality for convex bodies...
متن کاملOptimal decay of extremals for the fractional Sobolev inequality
We obtain the sharp asymptotic behavior at infinity of extremal functions for the fractional critical Sobolev embedding.
متن کاملAn Uniform Sobolev Inequality under Ricci Flow
Abstract. Let M be a compact Riemannian manifold and the metrics g = g(t) evolve by the Ricci flow. We prove the following result. The Sobolev imbedding by Aubin or Hebey, perturbed by a scalar curvature term and modulo sharpness of constants, holds uniformly for (M, g(t)) for all time if the Ricci flow exists for all time; and if the Ricci flow develops a singularity in finite time, then the s...
متن کاملSobolev Regularity and an Enhanced Jensen Inequality
We derive a new criterion for a real-valued function u to be in the Sobolev space W 1,2(Rn). This criterion consists of comparing the value of a functional R f(u) with the values of the same functional applied to convolutions of u with a Dirac sequence. The difference of these values converges to zero as the convolutions approach u, and we prove that the rate of convergence to zero is connected...
متن کاملPointwise Characterizations of Hardy-sobolev Functions
We establish pointwise characterizations of functions in the HardySobolev spaces H within the range p ∈ (n/(n + 1), 1]. In particular, a locally integrable function u belongs to H(R) if and only if u ∈ L(R) and it satisfies the Hajlasz type condition |u(x)− u(y)| ≤ |x − y|(h(x) + h(y)), x, y ∈ R \ E, where E is a set of measure zero and h ∈ L(R). We also investigate HardySobolev spaces on subdo...
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: 2020
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2020.124143