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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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.
V. M. Tikhomirov (1989)
Banach Center Publications
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Andrea Cianchi, Luboš Pick, Lenka Slavíková (2014)
Banach Center Publications
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We survey results from the paper [CPS] in which we developed a new sharp iteration method and applied it to show that the optimal Sobolev embeddings of any order can be derived from isoperimetric inequalities. We prove thereby that the well-known link between first-order Sobolev embeddings and isoperimetric inequalities translates to embeddings of any order, a fact that had not been known before. We show a general reduction principle that reduces Sobolev type inequalities of any order...
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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Zalgaller, V.A. (2005)
Journal of Mathematical Sciences (New York)
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Matteo Bonforte, Gabriele Grillo (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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We investigate the connection between certain logarithmic Sobolev inequalities and generalizations of Gagliardo-Nirenberg inequalities. A similar connection holds between reverse logarithmic Sobolev inequalities and a new class of reverse Gagliardo-Nirenberg inequalities.
Ershov, Yu.L., Kutateladze, S.S. (2009)
Sibirskij Matematicheskij Zhurnal
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B. Franchi, S. Gallot, R.L. Wheeden (1994)
Mathematische Annalen
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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.
Crăciunaş, Petru Teodor (1996)
General Mathematics
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Morosi, Carlo, Pizzocchero, Livio (2001)
Journal of Inequalities and Applications [electronic only]
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Radosław Adamczak (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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A. Pełczyński, K. Senator (1986)
Studia 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.
Michel Ledoux (1999)
Séminaire de probabilités de Strasbourg
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