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Sobolev inequalities on homogeneous spaces
Potential Analysis, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
BIROLI, MARCO, MOSCO U.
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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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Distributions and Sobolev Spaces [PDF]
, 2015 We have seen the concept of Dirac measure arising in connection with the fundamental solutions of the diffusion and the wave equations. Another interesting situation is the following, where the Dirac measure models a mechanical impulse.
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Embeddings of Anisotropic Sobolev Spaces
Archive for Rational Mechanics and Analysis, 1986This paper deals with the approximation and the entropy numbers of the embedding I of an anisotropic Sobolev space \(W^{r,p}(\Omega)\) into an Orlicz space \(L^{\phi}(\Omega)\), where \(\Omega\) is an open subset of \({\mathbb{R}}^ n\).
David E. Edmunds, R. M. Edmunds
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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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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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On one generalization of Sobolev spaces
Siberian Mathematical Journal, 1998In [Potential Anal. 5, No. 4, 403-415 (1996; Zbl 0859.46022)], \textit{P. Hajłasz} defined the Sobolev space \(S^1_p(X)\) on an arbitrary metric space.
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