About existence, symmetry and symmetry breaking for extremal functions of some interpolation functional inequalities
Esteban, Maria J.; Dolbeault, Jean (2012), About existence, symmetry and symmetry breaking for extremal functions of some interpolation functional inequalities, in Karlsen, Kenneth H.; Holden, Helge, Nonlinear Partial Differential Equations - The Abel Symposium 2010, Springer : Berlin, p. 117-130. http://dx.doi.org/10.1007/978-3-642-25361-4_6
Type
Chapitre d'ouvrageExternal document link
http://hal.archives-ouvertes.fr/hal-00539019/fr/Date
2012Book title
Nonlinear Partial Differential Equations - The Abel Symposium 2010Book author
Karlsen, Kenneth H.; Holden, HelgePublisher
Springer
Series title
Abel SymposiaSeries number
vol.7Published in
Berlin
ISBN
978-3-642-25360-7
Number of pages
360Pages
117-130
Publication identifier
Metadata
Show full item recordAbstract (EN)
This article 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 in collaboration with M. del Pino, S. Filippas, M. Loss, G. Tarantello and A. Tertikas. Here we put the highlights on a symmetry breaking result: extremals of some inequalities are not radially symmetric in regions where the symmetric extremals are linearly stable. Special attention is paid to the study of the critical cases for (CKN) and (WLH).Subjects / Keywords
optimal constants; compactness; existence; linearization; Emden-Fowler transformation; symmetry breaking; radial symmetry; extremal functions; logarithmic Sobolev inequality; logarithmic Hardy inequality; Gagliardo-Nirenberg inequality; Caffarelli-Kohn-Nirenberg inequalityRelated items
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Dolbeault, Jean; Esteban, Maria J. (2011) Communication / Conférence
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