Strokes of the biography of A. D. Alexandrov.
Kutateladze, S.S. (2001)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Displaying similar documents to “Variable Sobolev capacity and the assumptions on the exponent”
Strokes of the biography of A. D. Alexandrov.
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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.
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Toni Heikkinen, Pekka Koskela, Heli Tuominen (2007)
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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.
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We survey recent dimension-invariant imbedding theorems for Sobolev spaces.
Fifty years of the Siberian Division of the Russian Academy of Sciences.
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A. Benedek, R. Panzone (1990)
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Numerical Computation of Least Constants for the Sobolev Inequality.
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An estimate in the spirit of Poincaré's inequality
Augusto C. Ponce (2004)
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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 , 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.
On embeddings and traces in Sobolev spaces with weights of power type
Jiří Rákosník (1989)
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Hölder quasicontinuity of Sobolev functions on metric spaces.
Piotr Hajlasz, Juha Kinnunen (1998)
Revista Matemática Iberoamericana
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We prove that every Sobolev function defined on a metric space coincides with a Hölder continuous function outside a set of small Hausdorff content or capacity. Moreover, the Hölder continuous function can be chosen so that it approximates the given function in the Sobolev norm. This is a generalization of a result of Malý [Ma1] to the Sobolev spaces on metric spaces [H1].