A look on some results about Camassa–Holm type equations

Igor Leite Freire

Displaying similar documents to “A look on some results about Camassa–Holm type equations”

Variable Sobolev capacity and the assumptions on the exponent

Petteri Harjulehto, Peter Hästö, Mika Koskenoja, Susanna Varonen (2005)

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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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Dimension-invariant Sobolev imbeddings

Miroslav Krbec, Hans-Jürgen Schmeisser (2011)

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We survey recent dimension-invariant imbedding theorems for Sobolev spaces.

Fifty years of Siberian Mathematical Journal.

Ershov, Yu.L., Kutateladze, S.S. (2009)

Sibirskij Matematicheskij Zhurnal

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The sharp Sobolev inequality in quantitative form

Andrea Cianchi, Nicola Fusco, F. Maggi, A. Pratelli (2009)

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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.

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.

Some remarks on relative diameters

V. M. Tikhomirov (1989)

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On the Sobolev spaces I.

Crăciunaş, Petru Teodor (1996)

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On the intersection of Sobolev spaces

A. Benedek, R. Panzone (1990)

Colloquium Mathematicae

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An estimate in the spirit of Poincaré's inequality

Augusto C. Ponce (2004)

Journal of the European Mathematical Society

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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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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.

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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Weighted Sobolev spaces and capacity.

Kilpeläinen, Tero (1994)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

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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.

Tangential limits of monotone Sobolev functions.

Mizuta, Yoshihiro (1995)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

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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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On embeddings and traces in Sobolev spaces with weights of power type

Jiří Rákosník (1989)

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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 $ℝ^{n}$ , 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.

Hessian determinants as elements of dual Sobolev spaces

Teresa Radice (2014)

Studia Mathematica

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In this short note we present new integral formulas for the Hessian determinant. We use them for new definitions of Hessian under minimal regularity assumptions. The Hessian becomes a continuous linear functional on a Sobolev space.