Results 21 to 30 of about 1,128 (190)
Hardy’s inequalities for Sobolev functions [PDF]
Mathematical Research Letters, 1997 In this interesting paper, the authors develop a natural approach to estimates for Sobolev functions using fractional maximal operators. While some of the basic underlying estimates are known, the authors develop the subject systematically and decover new results or produce new proofs for known ones.
Kinnunen, Juha, Martio, Olli
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Sobolev inequalities for products of powers [PDF]
Transactions of the American Mathematical Society, 1989 The paper gives sufficient conditions on a pair of weight functions u, v in \({\mathbb{R}}^ n\), \(n>1\), so that the Sobolev inequality \[ (\int | f(x)|^ q u(x)dx)^{1/q}\leq C(\int | \nabla f(x)|^ p v(x)dx)^{1/p} \] holds for every \(f\in C^{\infty}_ 0({\mathbb{R}}^ n)\) with ...
Gatto, A. Eduardo, Wheeden, Richard L.
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Weighted Variable Exponent Sobolev spaces on metric measure spaces
Moroccan Journal of Pure and Applied Analysis, 2018 In this article we define the weighted variable exponent-Sobolev spaces on arbitrary metric spaces, with finite diameter and equipped with finite, positive Borel regular outer measure.
Hassib Moulay Cherif, Akdim Youssef
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Remarks on a Hardy–Sobolev inequality
Comptes Rendus. Mathématique, 2003 We compute the optimal constant for a generalized Hardy–Sobolev inequality, and using the product of two symmetrizations we present an elementary proof of the symmetries of some optimal functions. This inequality was motivated by a nonlinear elliptic equation arising in astrophysics.
Smets, D, Willem, M, SECCHI, SIMONE
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Sobolev inequality with non-uniformly degenerating gradient
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper we prove the following weighted Sobolev inequality in a bounded domain $\Omega\subset \mathbb{R}^n$, $ n\geq 1$, of a homogeneous space $(\mathbb{R}^n, \rho, wdx)$, under suitable compatibility conditions on the positive weight functions $(
Farman Mamedov, Sara Monsurrò
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Hypercontractive semigroups and Sobolev’s inequality [PDF]
Transactions of the American Mathematical Society, 1975 If H ⩾ 0 ...
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The Minimal Perimeter of a Log-Concave Function
Mathematics, 2020 Inspired by the equivalence between isoperimetric inequality and Sobolev inequality, we provide a new connection between geometry and analysis. We define the minimal perimeter of a log-concave function and establish a characteristic theorem of this ...
Niufa Fang, Zengle Zhang
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A modified Φ-Sobolev inequality for canonical Lévy processes and its applications
Modern Stochastics: Theory and Applications, 2023 A new modified Φ-Sobolev inequality for canonical ${L^{2}}$-Lévy processes, which are hybrid cases of the Brownian motion and pure jump-Lévy processes, is developed.
Noriyoshi Sakuma, Ryoichi Suzuki
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Symmetrization inequalities and Sobolev embeddings [PDF]
Proceedings of the American Mathematical Society, 2006 We prove new extended forms of the Pólya-Szegö symmetrization principle. As a consequence new sharp embedding theorems for generalized Besov spaces are proved, including a sharpening of the limiting cases of the classical Sobolev embedding theorem. In particular, a surprising self-improving property of certain Sobolev embeddings is uncovered.
Martín i Pedret, Joaquim, Milman, Mario
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Журнал Белорусского государственного университета: Математика, информатика, 2020 Let (X, d, µ) be a doubling metric measure space with doubling dimension γ, i. e. for any balls B(x, R) and B(x, r), r < R, following inequality holds µ(B(x, R)) ≤ aµ (R/r)γµ(B(x, r)) for some positive constants γ and aµ.
Sergey A. Bondarev
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