A diagonal embedding theorem for function spaces with dominating mixed smoothness properties
Hans Triebel (1989)
Banach Center Publications
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Displaying similar documents to “Mixed norms and Sobolev type inequalities”
A diagonal embedding theorem for function spaces with dominating mixed smoothness properties
Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed -norm.
Weidemaier, Peter (2002)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Strokes of the biography of A. D. Alexandrov.
Kutateladze, S.S. (2001)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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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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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.
Fifty years of Siberian Mathematical Journal.
Ershov, Yu.L., Kutateladze, S.S. (2009)
Sibirskij Matematicheskij Zhurnal
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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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Anisotropic Sobolev inequalities
Robert A. Adams (1988)
Časopis pro pěstování matematiky
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On the Sobolev spaces I.
Crăciunaş, Petru Teodor (1996)
General Mathematics
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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.
Extrapolation of Sobolev imbeddings.
M. Krbec (1997)
Collectanea Mathematica
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We survey recent results on limiting imbeddings [sic] of Sobolev spaces, particularly, those concerning weakening of assumptions on integrability of derivatives, considering spaces with dominating mixed derivatives and the case of weighted spaces.
On the general Brunn-Minkowski theorem.
Schneider, Rolf (1993)
Beiträge zur Algebra und Geometrie
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Some remarks on relative diameters
V. M. Tikhomirov (1989)
Banach Center Publications
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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.
A sharp iteration principle for higher-order Sobolev embeddings
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...
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.
Direct and Reverse Gagliardo-Nirenberg Inequalities from Logarithmic Sobolev Inequalities
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.