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Improved interpolation inequalities and stability

Dolbeault, Jean; Esteban, Maria J. (2020), Improved interpolation inequalities and stability, Advanced Nonlinear Studies, 20, 2, p. 277–291. 10.1515/ans-2020-2080

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Advanced Nonlinear Studies
Volume
20
Number
2
Publisher
De Gruyter
Published in
Paris
Pages
277–291
Publication identifier
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Author(s)
Dolbeault, Jean cc
Esteban, Maria J. cc
Abstract (EN)
For exponents in the subcritical range, we revisit some optimal interpolation inequalities on the sphere with carré du champ methods and use the remainder terms to produce improved inequalities. The method provides us with lower estimates of the optimal constants in the symmetry breaking range and stability estimates for the optimal functions. Some of these results can be reformulated in the Euclidean space using the stereographic projection.
Subjects / Keywords
Sobolev inequality; Gagliardo-Nirenberg inequalities; Interpolation; log- arithmic Sobolev inequality; Poincaré inequality; heat equation; nonlinear diffusion