Weighted interpolation inequalities: a perturbation approach
Dolbeault, Jean; Muratori, Matteo; Nazaret, Bruno (2017), Weighted interpolation inequalities: a perturbation approach, Mathematische Annalen, 369, 3-4, p. 1237-1270. 10.1007/s00208-016-1480-4
Type
Article accepté pour publication ou publiéExternal document link
http://arxiv.org/abs/1509.09127v1Date
2017Journal name
Mathematische AnnalenVolume
369Number
3-4Publisher
B. G. Teubner
Published in
Paris
Pages
1237-1270
Publication identifier
Metadata
Show full item recordAbstract (EN)
We study optimal functions in a family of Caffarelli-Kohn-Niren-berg inequalities with a power-law weight, in a regime for which standardsymmetrization techniques fail. We establish the existence of optimal func-tions, study their properties and prove that they are radialwhen the powerin the weight is small enough. Radial symmetry up to translations is truefor the limiting case where the weight vanishes, a case whichcorresponds toa well-known subfamily of Gagliardo-Nirenberg inequalities. Our approach isbased on a concentration-compactness analysis and on a perturbation methodwhich uses a spectral gap inequality. As a consequence, we prove that optimalfunctions are explicit and given by Barenblatt-type profiles in the perturbativeregime.Subjects / Keywords
Functional inequalities; Weights; Optimal functions; Best constants; Symmetry; Concentration-compactness; Gamma-convergenceRelated items
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Bonforte, Matteo; Dolbeault, Jean; Muratori, Matteo; Nazaret, Bruno (2017) Article accepté pour publication ou publié
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Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2023) Article accepté pour publication ou publié
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Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2020) Document de travail / Working paper
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Bonforte, Matteo; Dolbeault, Jean; Nazaret, Bruno; Simonov, Nikita (2020) Document de travail / Working paper