Improved Interpolation Inequalities and Stability

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.

Keywords

• interpolation
• gagliardo–nirenberg inequalities
• sobolev inequality
• logarithmic sobolev inequality
• poincaré inequality
• heat equation
• nonlinear diffusion
• 26d10
• 46e35
• 58e35