Results 291 to 300 of about 5,040,927 (317)
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AN ATOMIC DECOMPOSITION FOR THE HARDY-SOBOLEV SPACE
, 2007We define a Hardy-Sobolev space and give its atomic decomposition. As an application of the decomposition we prove a div-curl lemma.
Zengjian Lou, Shouzhi Yang
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Quaestiones Mathematicae, 2005
The present paper is devoted to discrete analogues of Sobolev spaces of smooth functions. The discrete analogues that we consider are spaces of functions on vertex sets of graphs. Such spaces have applications in Graph Theory, Metric Geometry and Convex Geometry. We present known and prove some new results on Banach-space-theoretical properties of such
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The present paper is devoted to discrete analogues of Sobolev spaces of smooth functions. The discrete analogues that we consider are spaces of functions on vertex sets of graphs. Such spaces have applications in Graph Theory, Metric Geometry and Convex Geometry. We present known and prove some new results on Banach-space-theoretical properties of such
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2014
Chapter 6 is devoted to the precise definitions and statements of Sobolev and Besov spaces of L p type with some detailed proofs. One of the most useful ways of measuring differentiability properties of functions is in terms of $$L^{p}$$ norms, and is provided by the Sobolev spaces.
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Chapter 6 is devoted to the precise definitions and statements of Sobolev and Besov spaces of L p type with some detailed proofs. One of the most useful ways of measuring differentiability properties of functions is in terms of $$L^{p}$$ norms, and is provided by the Sobolev spaces.
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A Sobolev space theory of SPDEs with constant coefficients on a half line
, 1999Equations of the form $du=(a^{ij}u_{x^{i}x^{j}} +D_{i}f^{i})\,dt+\sum_{k}(\sigma^{ik}u_{x^{i}} +g^{k})\,dw^{k}_{t}$ are considered for t > 0 and $x\in\bR^{d}_{+}$.
N. Krylov, S. Lototsky
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Sobolev Spaces on Metric Spaces [PDF]
, 2001 We have seen that if u is a smooth function defined on a ball B in ℝ n (possibly with infinite radius so that B = ℝ n ), then the inequality $$ \left| {u(x) - u(y)} \right| \leqslant C (n)(I_1 \left| {\nabla u} \right|(x) + I_1 \left| {\nabla u} \right|(y)) $$ (5.1) holds for each pair of points x, y in B, where I1 is the Riesz potential.
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The Lebesgue and Sobolev Spaces
2014The main focus of chapter 8 is the establishment of basic concepts on Lebesgue and Sobolev spaces. The results developed include the classical Sobolev imbedding and trace theorems for a special class of domains.
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Fractional Sobolev spaces and topology
Nonlinear Analysis: Theory, Methods & Applications, 2008Abstract Consider the Sobolev class W s , p ( M , N ) where M and N are compact manifolds, and p ≥ 1 , s ∈ ( 0 , 1 + 1 / p ) . We present a necessary and sufficient condition for two maps u and v in W s , p ( M , N ) to be continuously connected in W s ,
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Description of traces of functions in the Sobolev space with a Muckenhoupt weight
, 2014A. Tyulenev
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A Poincaré inequality in a Sobolev space with a variable exponent
, 2011P. G. Ciarlet, G. Dincă
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Remarks on Gagliardo–Nirenberg type inequality with critical Sobolev space and BMO
, 2008H. Kozono, H. Wadade
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