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Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants

Dolbeault, Jean; Esteban, Maria J. (2011), Extremal functions in some interpolation inequalities: Symmetry, symmetry breaking and estimates of the best constants, in Exner, Pavel, Mathematical results in quantum physics. Proceedings of the QMath11 Conference Hradec Králové, Czech Republic, 6 - 10 September 2010, World Scientific, p. 178-182. http://dx.doi.org/10.1142/9789814350365_0017

Type
Communication / Conférence
External document link
http://arxiv.org/abs/1009.5619v1
Date
2011
Conference title
Conference on mathematical results in quantum physics (QMATH-11)
Conference date
2010-09
Conference city
Hradec Králové
Conference country
République tchèque
Book title
Mathematical results in quantum physics. Proceedings of the QMath11 Conference Hradec Králové, Czech Republic, 6 - 10 September 2010
Book author
Exner, Pavel
Publisher
World Scientific
Pages
178-182
Publication identifier
http://dx.doi.org/10.1142/9789814350365_0017
Metadata
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Author(s)
Dolbeault, Jean cc
Esteban, Maria J. cc
Abstract (EN)
This contribution is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg (CKN) and weighted logarithmic Hardy (WLH) inequalities. These results have been obtained in a series of papers [1–5] in collaboration with M. del Pino, S. Filippas, M. Loss, G. Tarantello and A. Tertikas and are presented from a new viewpoint.
Subjects / Keywords
Caffarelli-Kohn-Nirenberg inequality; Gagliardo-Nirenberg inequality; logarithmic Hardy inequality; logarithmic Sobolev inequality; extremal functions; radial symmetry; symmetry breaking; Emden-Fowler transformation; linearization; existence; compactness; optimal constants

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    Tertikas, Achilles; Tarantello, Gabriella; Esteban, Maria J.; Dolbeault, Jean (2011) Article accepté pour publication ou publié
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    Dolbeault, Jean; Esteban, Maria J.; Tarantello, Gabriella (2008) Article accepté pour publication ou publié
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    Symmetry of extremals of functional inequalities via spectral estimates for linear operators 
    Loss, Michael; Esteban, Maria J.; Dolbeault, Jean (2012) Article accepté pour publication ou publié
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