Results 31 to 40 of about 4,705,780 (288)
Degree and Sobolev spaces [PDF]
Topological Methods in Nonlinear Analysis, 1999 Let $u$ belong (for example) to $W^{1,n+1}(S^n\times \Lambda, S^n)_{\lambda\in\Lambda}$ where $\Lambda$ is a connected open set in ${\mathbb R}^k$. For a.e. the map $x\mapsto u(x,\lambda)$ is continuous from $S^n$ into $S^n$ and therefore its (Brouwer) degree is well defined. We prove that this degree is independent of $\lambda$ a.e.
Brezis, Haïm +3 more
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Multiplication in Sobolev spaces, revisited [PDF]
Arkiv för Matematik, 2021 25 pages, no figures.
Michael Holst, A. Behzadan
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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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Uhlenbeck’s Decomposition in Sobolev and Morrey–Sobolev Spaces [PDF]
Results in Mathematics, 2018 We present a self-contained proof of Uhlenbeck's decomposition theorem for $ \in L^p(\mathbb{B}^n,so(m)\otimes ^1\mathbb{R}^n)$ for $p\in (1,n)$ with Sobolev type estimates in the case $p \in[n/2,n)$ and Morrey-Sobolev type estimates in the case $p\in (1,n/2)$.
Anna Zatorska-Goldstein +1 more
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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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Improved Sobolev Inequalities and Muckenhoupt weights on stratified Lie groups [PDF]
, 2010 We study in this article the Improved Sobolev inequalities with Muckenhoupt weights within the framework of stratified Lie groups. This family of inequalities estimate the Lq norm of a function by the geometric mean of two norms corresponding to Sobolev ...
Chamorro, Diego
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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
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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$L^p$-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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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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