Results 21 to 30 of about 5,230,860 (246)
$L^p$-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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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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On some nonlinear anisotropic elliptic equations in anisotropic Orlicz space [PDF]
Arab Journal of Mathematical Sciences, 2023 Purpose – In the present paper, the authors will discuss the solvability of a class of nonlinear anisotropic elliptic problems (P), with the presence of a lower-order term and a non-polynomial growth which does not satisfy any sign condition which is ...
Omar Benslimane +2 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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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
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GEODESIC COMPLETENESS FOR SOBOLEV METRICS ON THE SPACE OF IMMERSED PLANE CURVES
Forum of Mathematics, Sigma, 2014 We study properties of Sobolev-type metrics on the space of immersed plane curves. We show that the geodesic equation for Sobolev-type metrics with constant coefficients of order 2 and higher is globally well-posed for smooth initial data as well as for ...
MARTINS BRUVERIS +2 more
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, 2013 In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the
A. Berlinet +19 more
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Final State Problem for the Dirac-Klein-Gordon Equations in Two Space Dimensions
Abstract and Applied Analysis, 2013 We study the final state problem for the Dirac-Klein-Gordon equations (DKG) in two space dimensions. We prove that if the nonresonance mass condition is satisfied, then the wave operator for DKG is well defined from a neighborhood at the origin in lower ...
Masahiro Ikeda
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