### Isoperimetric Inequalities and the Problem of Plateau.

K. Steffen (1976)

Mathematische Annalen

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K. Steffen (1976)

Mathematische Annalen

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Christer Borell (1983)

Mathematische Annalen

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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.

Shigeo Kawai (1992)

Mathematische Annalen

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M.L. Cartwright (1935)

Mathematische Annalen

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P.H. Diananda (1980)

Mathematische Annalen

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S. TANNO (1970/71)

Mathematische Annalen

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Rajendra Bhatia, John A.R. Holbrook (1988)

Mathematische Annalen

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Volker Vogelsang (1991)

Mathematische Annalen

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W. Hansen, V. Andrievskii (1992)

Mathematische Annalen

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Philip S. Crooke (1978)

Colloquium Mathematicae

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R.M. Redheffer (1957)

Mathematische Annalen

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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...

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

Journal of the European Mathematical Society

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Radosław Adamczak (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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T. Ando (1987/88)

Mathematische Annalen

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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.

V. M. Tikhomirov (1989)

Banach Center Publications

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