Maximal regularity for parabolic initial-boundary value problems in Sobolev spaces.
Giovanni Dore, Alberto Venni (1991)
Mathematische Zeitschrift
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Giovanni Dore, Alberto Venni (1991)
Mathematische Zeitschrift
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Н.В. Житарашу (1982)
Matematiceskie issledovanija
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V. I. Kolyada (2006)
Banach Center Publications
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We study mixed norm spaces that arise in connection with embeddings of Sobolev and Besov spaces. We prove Sobolev type inequalities in terms of these mixed norms. Applying these results, we obtain optimal constants in embedding theorems for anisotropic Besov spaces. This gives an extension of the estimate proved by Bourgain, Brezis and Mironescu for isotropic Besov spaces.
Hans Triebel (1989)
Banach Center Publications
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J. Chabrowski (1973)
Annales Polonici Mathematici
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Kutateladze, S.S. (2001)
Vladikavkazskiĭ Matematicheskiĭ 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.
Ershov, Yu.L., Kutateladze, S.S. (2009)
Sibirskij Matematicheskij Zhurnal
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Crăciunaş, Petru Teodor (1996)
General Mathematics
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Andrea Cianchi, Nicola Fusco, F. Maggi, A. Pratelli (2009)
Journal of the European Mathematical Society
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V. M. Tikhomirov (1989)
Banach Center Publications
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Hans Wallin (1991)
Manuscripta mathematica
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W. M. Zajączkowski
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The existence and uniqueness of solutions of an initial-boundary value problem for the second order linear parabolic system which appears in free boundary problems for compressible Navier-Stokes equations are proved. Moreover, an estimate in anisotropic Sobolev-Slobodetskii spaces with noninteger derivatives is found. The existence and regularity of solutions are shown by means of a regularizer in the same way as in the case of general parabolic systems. However, the problem must be...
Jiří Rákosník (1989)
Banach Center Publications
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A. Pełczyński, K. Senator (1986)
Studia Mathematica
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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.
A. Benedek, R. Panzone (1990)
Colloquium Mathematicae
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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.
Ershov, Yu.L., Kutateladze, S.S., Tajmanov, I.A. (2007)
Sibirskij Matematicheskij Zhurnal
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Kilpeläinen, Tero (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Miroslav Krbec, Hans-Jürgen Schmeisser (2011)
Banach Center Publications
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We survey recent dimension-invariant imbedding theorems for Sobolev spaces.