Symmetrization of Functions in Sobolev Spaces and The Isoperimetric Inequality.
Keijo Hildén (1976)
Manuscripta mathematica
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Keijo Hildén (1976)
Manuscripta mathematica
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Gérard Bourdaud (1988)
Manuscripta mathematica
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Jürgen Marschall (1987)
Manuscripta mathematica
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G. Dal Maso, Anneliese Defranceschi (1992)
Manuscripta mathematica
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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.
Kutateladze, S.S. (2001)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Jiří Rákosník (1989)
Banach Center Publications
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Giovanni Mancini, Roberta Musina (1987)
Manuscripta mathematica
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Ershov, Yu.L., Kutateladze, S.S. (2009)
Sibirskij Matematicheskij Zhurnal
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V. M. Tikhomirov (1989)
Banach Center Publications
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Wolf von Wahl (1977)
Manuscripta mathematica
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A. Benedek, R. Panzone (1990)
Colloquium Mathematicae
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Crăciunaş, Petru Teodor (1996)
General Mathematics
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Andrea Cianchi, Nicola Fusco, F. Maggi, A. Pratelli (2009)
Journal of the European Mathematical Society
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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.
Rainer Schumann (1989)
Manuscripta 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.
Tosio Kato (1979)
Manuscripta mathematica
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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.
Igor Leite Freire (2021)
Communications in Mathematics
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We present an overview of some contributions of the author regarding Camassa--Holm type equations. We show that an equation unifying both Camassa--Holm and Novikov equations can be derived using the invariance under certain suitable scaling, conservation of the Sobolev norm and existence of peakon solutions. Qualitative analysis of the two-peakon dynamics is given.