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Extremal functions and symmetry breaking in Caffarelli-Kohn-Nirenberg inequalities

Dolbeault, Jean (2010), Extremal functions and symmetry breaking in Caffarelli-Kohn-Nirenberg inequalities, Oberwolfach Reports, 7, 1, p. 330-334

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00456919/en/
Date
2010
Journal name
Oberwolfach Reports
Volume
7
Number
1
Publisher
European Mathematical Society
Pages
330-334
Metadata
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Author(s)
Dolbeault, Jean cc
Abstract (EN)
Results on extremal functions of some interpolation inequalities introduced by Caffarelli, Kohn and Nirenberg and of weighted logarithmic Hardy inequalities are briefly reviewed. Some results of radial symmetry or of symmetry breaking are sketched, which result in the statement of an open question. These notes are based on a collaboration with M. Esteban, M. Loss, G. Tarantello and A. Tertikas.
Subjects / Keywords
Caffarelli-Kohn-Nirenberg inequalities