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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A. Pełczyński, K. Senator (1986)
Studia Mathematica
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Ershov, Yu.L., Kutateladze, S.S. (2009)
Sibirskij Matematicheskij 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.
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].
Andrea Cianchi, Nicola Fusco, F. Maggi, A. Pratelli (2009)
Journal of the European Mathematical Society
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Francesca Lascialfari, David Pardo (2002)
Rendiconti del Seminario Matematico della Università di Padova
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Kutateladze, S.S. (2001)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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David Edmunds, Jiří Rákosník (2000)
Studia Mathematica
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A. Benedek, R. Panzone (1990)
Colloquium Mathematicae
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V. M. Tikhomirov (1989)
Banach Center Publications
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Bogdan Bojarski, Piotr Hajłasz (1993)
Studia Mathematica
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We get a class of pointwise inequalities for Sobolev functions. As a corollary we obtain a short proof of Michael-Ziemer’s theorem which states that Sobolev functions can be approximated by functions both in norm and capacity.
P. Szeptycki (1956)
Studia Mathematica
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Ershov, Yu.L., Kutateladze, S.S., Tajmanov, I.A. (2007)
Sibirskij Matematicheskij Zhurnal
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Tullio Valent (1985)
Rendiconti del Seminario Matematico della Università di Padova
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Crăciunaş, Petru Teodor (1996)
General Mathematics
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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.