### On a Class of Weighted Sobolev's Spaces

P. Bolley, J. Camus, The Lai Pham (1978)

Publications mathématiques et informatique de Rennes

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P. Bolley, J. Camus, The Lai Pham (1978)

Publications mathématiques et informatique de Rennes

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Petr Gurka, Alois Kufner (1989)

Banach Center Publications

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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].

Ritva Hurri (1990)

Mathematica Scandinavica

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Anders, Maz'ya, V. Carlsson (1994)

Mathematica Scandinavica

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Salvatore Leonardi (1994)

Rendiconti del Seminario Matematico della Università di Padova

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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.

Mahavier, W.T. (1999)

Southwest Journal of Pure and Applied Mathematics [electronic only]

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Brown, R.C. (2008)

Banach Journal of Mathematical Analysis [electronic only]

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Cahiers du Bureau universitaire de recherche opérationnelle Série Recherche

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Agnieszka Kałamajska (1994)

Studia Mathematica

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G. Greaves (1985)

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Geraldo Soares De Souza (1990)

Colloquium Mathematicae

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Bichegkuev, M.S. (1999)

Vladikavkazskiĭ Matematicheskiĭ Zhurnal

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