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Weighted Sobolev Spaces And Capacity
, 1994
"... . We discuss the role of capacity in the pointwise definition of functions in Sobolev spaces involving weights of Muckenhoupt's A p class. In particular, it is shown that Sobolev functions possess Lebesgue points quasieverywhere with respect to an appropriate capacity. Introduction Let\Omega ..."
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. We discuss the role of capacity in the pointwise definition of functions in Sobolev spaces involving weights of Muckenhoupt's A p class. In particular, it is shown that Sobolev functions possess Lebesgue points quasieverywhere with respect to an appropriate capacity. Introduction Let
Compact Traces in Weighted Sobolev Spaces
, 1995
"... . We study trace operators in weighted Sobolev spaces W 1;p (\Omega\Gamma v 0 ; v 1 ) ,! L q (@ w) for sufficiently regular unbounded domains\Omega ae IR N with noncompact boundary. We show that under certain conditions on the weight functions v 0 ; v 1 ; w, this operator is compact. This re ..."
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Cited by 6 (1 self)
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. We study trace operators in weighted Sobolev spaces W 1;p (\Omega\Gamma v 0 ; v 1 ) ,! L q (@ w) for sufficiently regular unbounded domains\Omega ae IR N with noncompact boundary. We show that under certain conditions on the weight functions v 0 ; v 1 ; w, this operator is compact
THE OSEEN EQUATIONS IN Rn AND WEIGHTED SOBOLEV SPACES
"... Abstract. In this paper, we study the nonhomogeneous Oseen equations in Rn. We prove an existence and uniqueness result in weighted Sobolev spaces. As the main tool, we prove an existence and uniqueness theorem of a scalar model of those equations. ..."
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Abstract. In this paper, we study the nonhomogeneous Oseen equations in Rn. We prove an existence and uniqueness result in weighted Sobolev spaces. As the main tool, we prove an existence and uniqueness theorem of a scalar model of those equations.
1 Weighted Sobolev spaces and embedding theorems
, 2007
"... In the present paper we study embedding operators for weighted Sobolev spaces whose weights satisfy the wellknown Muckenhoupt Apcondition. Sufficient conditions for boundedness and compactness of the embedding operators are obtained for smooth domains and domains with boundary singularities. The p ..."
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In the present paper we study embedding operators for weighted Sobolev spaces whose weights satisfy the wellknown Muckenhoupt Apcondition. Sufficient conditions for boundedness and compactness of the embedding operators are obtained for smooth domains and domains with boundary singularities
Characterization of traces of the weighted Sobolev space
 W 1,p(Ω, dM ) on M . Czechoslovak Math. J
, 1993
"... This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DMLCZ: The Czech Digital ..."
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Cited by 10 (0 self)
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This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DMLCZ: The Czech Digital
Elliptic equations in weighted Sobolev spaces on unbounded domains,
 Int. J. Math. Math. Sci.,
, 2008
"... We study in this paper a class of secondorder linear elliptic equations in weighted Sobolev spaces on unbounded domains of R n , n ≥ 3. We obtain an a priori bound, and a regularity result from which we deduce a uniqueness theorem. ..."
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Cited by 3 (2 self)
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We study in this paper a class of secondorder linear elliptic equations in weighted Sobolev spaces on unbounded domains of R n , n ≥ 3. We obtain an a priori bound, and a regularity result from which we deduce a uniqueness theorem.
Potential Estimates and Imbedding Theorems for Weighted Sobolev Spaces.
"... This paper is concerned with imbeddings of weighted Sobolev spaces denoted by H1ƒ¿,p(Rnk•~Rk). Under some assumptions, the existence of imbeddings of H1ƒ¿,p(Rnk•~Rk) into Schauder spaces with weights denoted by SC0ƒ¿,ƒÉ(Rnk•~Rk) will be shown, where the weight functions concidered here are powers ..."
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This paper is concerned with imbeddings of weighted Sobolev spaces denoted by H1ƒ¿,p(Rnk•~Rk). Under some assumptions, the existence of imbeddings of H1ƒ¿,p(Rnk•~Rk) into Schauder spaces with weights denoted by SC0ƒ¿,ƒÉ(Rnk•~Rk) will be shown, where the weight functions concidered here
Weighted Sobolev spaces and regularity for polyhedral domains
, 2006
"... We prove a regularity result for the Poisson problem −∆u = f, u∂P = g on a polyhedral domain P ⊂ R3 using the Babuˇska–Kondratiev spaces Km a (P). These are weighted Sobolev spaces in which the weight is given by the distance to the set of edges [4, 29]. In particular, we show that there is no loss ..."
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Cited by 18 (10 self)
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We prove a regularity result for the Poisson problem −∆u = f, u∂P = g on a polyhedral domain P ⊂ R3 using the Babuˇska–Kondratiev spaces Km a (P). These are weighted Sobolev spaces in which the weight is given by the distance to the set of edges [4, 29]. In particular, we show
APPROXIMATION THEORY FOR WEIGHTED SOBOLEV SPACES ON CURVES VENANCIO
"... Abstract. In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete. We also prove the density of the polynomials in these spaces for nonclosed compact curves and, finally, we find conditions under which the multiplica ..."
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Abstract. In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete. We also prove the density of the polynomials in these spaces for nonclosed compact curves and, finally, we find conditions under which
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