Some remarks about the density of smooth functions in weighted Sobolev spaces.
Chiadò Piat, Valeria, Serra Cassano, Francesco (1994)
Journal of Convex Analysis
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Chiadò Piat, Valeria, Serra Cassano, Francesco (1994)
Journal of Convex Analysis
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P. Bolley, J. Camus, The Lai Pham (1978)
Publications mathématiques et informatique de Rennes
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Wojciech M. Zajączkowski (2002)
Applicationes Mathematicae
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Using the Il'in integral representation of functions, imbedding theorems for weighted anisotropic Sobolev spaces in 𝔼ⁿ are proved. By the weight we assume a power function of the distance from an (n-2)-dimensional subspace passing through the domain considered.
Stanislav Kračmar, Patrick Penel (2005)
Banach Center Publications
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We consider a generic scalar model for the Oseen equations in an exterior three-dimensional domain. We assume the case of a non-constant coefficient function. Using a variational approach we prove new regularity properties of a weak solution whose existence and uniqueness in anisotropically weighted Sobolev spaces were proved in [10]. Because we use some facts and technical tools proved in the above mentioned paper, we give also a brief review of its results and methods.
Antonio Avantaggiati, Paola Loreti (2009)
Bollettino dell'Unione Matematica Italiana
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In this paper we obtain a more general inequality with respect to a well known inequality due to Gagliardo (see [4], [5]). The inequality contained in [4], [5] has been extended to weighted spaces, obtained as cartesian product of measurable spaces. As application, we obtain a first order weighted Sobolev inequality. This generalize a previous result obtained in [2].
Salvatore Leonardi (1994)
Rendiconti del Seminario Matematico della Università di Padova
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Petr Gurka, Alois Kufner (1989)
Banach Center Publications
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Mahavier, W.T. (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Jiří Rákosník (1989)
Banach Center Publications
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Michael Langenbruch (1987)
Mathematische Zeitschrift
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Agnieszka Kałamajska (1994)
Studia Mathematica
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Kilpeläinen, Tero (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Brown, R.C. (1998)
Journal of Inequalities and Applications [electronic only]
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Silvana Marchi (1991)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We prove a sufficient condition of continuity at the boundary for quasiminima of degenerate type. W. P. Ziemer stated a Wiener-type criterion for the quasiminima defined by Giaquinta and Giusti. In this paper we extend the result of Ziemer to the case of weighted quasiminima, the weight being in the class of Muckenhoupt.