Fifty years of Siberian Mathematical Journal.
Ershov, Yu.L., Kutateladze, S.S. (2009)
Sibirskij Matematicheskij Zhurnal
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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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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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Crăciunaş, Petru Teodor (1996)
General Mathematics
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V. M. Tikhomirov (1989)
Banach Center Publications
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A. Pełczyński, K. Senator (1986)
Studia Mathematica
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Kilpeläinen, Tero (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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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.
Miroslav Krbec, Hans-Jürgen Schmeisser (2011)
Banach Center Publications
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We survey recent dimension-invariant imbedding theorems for Sobolev spaces.
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.
Mizuta, Yoshihiro (1995)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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A. Benedek, R. Panzone (1990)
Colloquium Mathematicae
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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.
J.T. Marti, M. Hegland (1986)
Numerische Mathematik
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Alicja Gąsiorowska (2011)
Banach Center Publications
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We prove asymptotic formulas for the behavior of Gelfand and Kolmogorov numbers of Sobolev embeddings between Besov and Triebel-Lizorkin spaces of radial distributions. Our method works also for Weyl numbers.
Jiří Rákosník (1989)
Banach Center Publications
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Alireza Ranjbar-Motlagh (2009)
Studia Mathematica
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The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.
Augusto C. Ponce (2004)
Journal of the European Mathematical Society
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Ivan Gentil (2008)
Annales de la faculté des sciences de Toulouse Mathématiques
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We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the Prékopa-Leindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on , with a strictly convex and super-linear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly convex potential as well as the Euclidean logarithmic Sobolev inequality.