Results 31 to 40 of about 4,722,250 (284)
$L^p$-Taylor approximations characterize the Sobolev space $W^{1,p}$ [PDF]
, 2015 In this note, we introduce a variant of Calder\'on and Zygmund's notion of $L^p$-differentiability - an \emph{$L^p$-Taylor approximation}. Our first result is that functions in the Sobolev space $W^{1,p}(\mathbb{R}^N)$ possess a first order $L^p$-Taylor ...
Spector, Daniel E.
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, 2017 The content of this paper is at the interplay between function spaces $L^{p(x)}$ and $W^{k, p(x)}$ with variable exponents and fractional Sobolev spaces $W^{s, p}$.
Anouar Bahrouni, Vicentiu D. Rădulescu
semanticscholar +1 more source
On the intersection of Sobolev spaces [PDF]
Colloquium Mathematicum, 1990 Assume \(1\leq p< \infty\), \(r\) and \(R\) are non-negative integers, \(r< R\), and \(\Omega\) is a bounded domain in \(\mathbb{R}^ n\). Let \(W^{p,r}\) be the Sobolev space of functions \(f\) in \(L^ p(\Omega)\) with distributional derivatives up to order \(r\) in \(L^ p(\Omega)\).
A. Benedek, R. Panzone
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Sobolev capacity on the space W1, p(⋅)(ℝn)
Journal of Function Spaces and Applications, 2003 We define Sobolev capacity on the generalized Sobolev space W1, p(⋅)(ℝn). It is a Choquet capacity provided that the variable exponent p:ℝn→[1,∞) is bounded away from 1 and ∞.
Petteri Harjulehto +3 more
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Sobolev spaces with non-Muckenhoupt weights, fractional elliptic operators, and applications [PDF]
, 2018 We propose a new variational model in weighted Sobolev spaces with non-standard weights and applications to image processing. We show that these weights are, in general, not of Muckenhoupt type and therefore the classical analysis tools may not apply ...
Antil, Harbir, Rautenberg, Carlos N.
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Entropy, 2018 We investigate the exponential convergence of a Markovian semigroup in the Zygmund space under the assumption of logarithmic Sobolev inequality. We show that the convergence rate is greater than the logarithmic Sobolev constant.
Ichiro Shigekawa
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New reproducing kernel functions in the reproducing kernel Sobolev spaces
AIMS Mathematics, 2020 In this paper we construct some new reproducing kernel functions in the reproducing kernel Sobolev space. These functions are new in the literature. We can solve many problems by these functions in the reproducing kernel Sobolev spaces.
Ali Akgül +2 more
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Concerning the pathological set in the context of probabilistic well-posedness
Comptes Rendus. Mathématique, 2021 We prove a complementary result to the probabilistic well-posedness for the nonlinear wave equation. More precisely, we show that there is a dense set $S$ of the Sobolev space of super-critical regularity such that (in sharp contrast with the ...
Sun, Chenmin, Tzvetkov, Nikolay
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Traces of multipliers in pairs of weighted Sobolev spaces
Journal of Function Spaces and Applications, 2005 We prove that the pointwise multipliers acting in a pair of fractional Sobolev spaces form the space of boundary traces of multipliers in a pair of weighted Sobolev space of functions in a domain.
Vladimir Maz'ya, Tatyana Shaposhnikova
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Long‐time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space [PDF]
, 2002 The authors compute the long-time asymptotics for solutions of the NLS equation just under the assumption that the initial data lies in a weighted Sobolev space. In earlier work (see e.g.
P. Deift, Xin Zhou
semanticscholar +1 more source