On embeddings and traces in Sobolev spaces with weights of power type
Jiří Rákosník (1989)
Banach Center Publications
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Jiří Rákosník (1989)
Banach Center Publications
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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.
Kilpeläinen, Tero (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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P. Bolley, J. Camus, The Lai Pham (1978)
Publications mathématiques et informatique de Rennes
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Petteri Harjulehto, Peter Hästö, Mika Koskenoja, Susanna Varonen (2005)
Banach Center Publications
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In a recent article the authors showed that it is possible to define a Sobolev capacity in variable exponent Sobolev space. However, this set function was shown to be a Choquet capacity only under certain assumptions on the variable exponent. In this article we relax these assumptions.
Andrea Cianchi, Nicola Fusco, F. Maggi, A. Pratelli (2009)
Journal of the European Mathematical Society
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V. M. Tikhomirov (1989)
Banach Center Publications
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Ershov, Yu.L., Kutateladze, S.S. (2009)
Sibirskij Matematicheskij Zhurnal
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Kutateladze, S.S. (2001)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Crăciunaş, Petru Teodor (1996)
General Mathematics
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Toni Heikkinen, Pekka Koskela, Heli Tuominen (2007)
Studia Mathematica
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We define a Sobolev space by means of a generalized Poincaré inequality and relate it to a corresponding space based on upper gradients.
A. Pełczyński, K. Senator (1986)
Studia Mathematica
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Mahavier, W.T. (1999)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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J.T. Marti, M. Hegland (1986)
Numerische Mathematik
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Valentino Magnani (2005)
Studia Mathematica
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In the geometries of stratified groups, we provide differentiability theorems for both functions of bounded variation and Sobolev functions. Proofs are based on a systematic application of the Sobolev-Poincaré inequality and the so-called representation formula.
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].
Ershov, Yu.L., Kutateladze, S.S., Tajmanov, I.A. (2007)
Sibirskij Matematicheskij Zhurnal
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Salvatore Leonardi (1994)
Rendiconti del Seminario Matematico della Università di Padova
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