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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Displaying similar documents to “Some remarks on relative diameters”
The sharp Sobolev inequality in quantitative form
Variable Sobolev capacity and the assumptions on the exponent
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.
Strokes of the biography of A. D. Alexandrov.
Kutateladze, S.S. (2001)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Fifty years of Siberian Mathematical Journal.
Ershov, Yu.L., Kutateladze, S.S. (2009)
Sibirskij Matematicheskij Zhurnal
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On the Sobolev spaces I.
Crăciunaş, Petru Teodor (1996)
General Mathematics
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Addendum to the paper "On isomorphisms of anisotropic Sobolev spaces with "classical Banach spaces" and a Sobolev type embedding theorem"
A. Pełczyński, K. Senator (1986)
Studia Mathematica
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Weighted Sobolev spaces and capacity.
Kilpeläinen, Tero (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Fifty years of the Siberian Division of the Russian Academy of Sciences.
Ershov, Yu.L., Kutateladze, S.S., Tajmanov, I.A. (2007)
Sibirskij Matematicheskij Zhurnal
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Sobolev-type spaces from generalized Poincaré inequalities
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.
Dimension-invariant Sobolev imbeddings
Miroslav Krbec, Hans-Jürgen Schmeisser (2011)
Banach Center Publications
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We survey recent dimension-invariant imbedding theorems for Sobolev spaces.
Differentiability from the representation formula and the Sobolev-Poincaré inequality
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.
Tangential limits of monotone Sobolev functions.
Mizuta, Yoshihiro (1995)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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On the intersection of Sobolev spaces
A. Benedek, R. Panzone (1990)
Colloquium Mathematicae
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Numerical Computation of Least Constants for the Sobolev Inequality.
J.T. Marti, M. Hegland (1986)
Numerische Mathematik
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A look on some results about Camassa–Holm type equations
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.
An isoperimetric bound for a Sobolev constant
Philip S. Crooke (1978)
Colloquium Mathematicae
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On embeddings and traces in Sobolev spaces with weights of power type
Jiří Rákosník (1989)
Banach Center Publications
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Gelfand and Kolmogorov numbers of embedding of radial Besov and Sobolev spaces
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.
An embedding theorem for Sobolev type functions with gradients in a Lorentz space
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.
From the Prékopa-Leindler inequality to modified logarithmic Sobolev inequality
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.