The sharp Sobolev inequality in quantitative form
Andrea Cianchi, Nicola Fusco, F. Maggi, A. Pratelli (2009)
Journal of the European Mathematical Society
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Andrea Cianchi, Nicola Fusco, F. Maggi, A. Pratelli (2009)
Journal of the European Mathematical Society
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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.
V. M. Tikhomirov (1989)
Banach Center Publications
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Kutateladze, S.S. (2001)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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V. I. Kolyada (2006)
Banach Center Publications
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We study mixed norm spaces that arise in connection with embeddings of Sobolev and Besov spaces. We prove Sobolev type inequalities in terms of these mixed norms. Applying these results, we obtain optimal constants in embedding theorems for anisotropic Besov spaces. This gives an extension of the estimate proved by Bourgain, Brezis and Mironescu for isotropic Besov spaces.
Ershov, Yu.L., Kutateladze, S.S. (2009)
Sibirskij Matematicheskij Zhurnal
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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.
Crăciunaş, Petru Teodor (1996)
General Mathematics
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Hans Triebel (1989)
Banach Center Publications
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A. Pełczyński, K. Senator (1986)
Studia Mathematica
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R. Telgársky (1968)
Colloquium Mathematicae
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Augusto C. Ponce (2004)
Journal of the European Mathematical Society
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Kilpeläinen, Tero (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Ershov, Yu.L., Kutateladze, S.S., Tajmanov, I.A. (2007)
Sibirskij Matematicheskij Zhurnal
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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. Benedek, R. Panzone (1990)
Colloquium Mathematicae
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Mizuta, Yoshihiro (1995)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Miroslav Krbec, Hans-Jürgen Schmeisser (2011)
Banach Center Publications
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We survey recent dimension-invariant imbedding theorems for Sobolev spaces.
Ch. Konstadilaki, I. L. Reilly (1991)
Matematički Vesnik
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K. P. Chew, H. P. Tan (1972)
Publications de l'Institut Mathématique
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