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Uthscsa Press, Advanced Nonlinear Studies, 0(0), 2020

DOI: 10.1515/ans-2020-2080

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Improved Interpolation Inequalities and Stability

Journal article published in 2020 by Jean Dolbeault ORCID, Maria J. Esteban ORCID
This paper is available in a repository.
This paper is available in a repository.

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Abstract

Abstract 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.