Logarithmic Sobolev and interpolation inequalities on the sphere: Constructive stability results
Giovanni Brigati, Jean Dolbeault, Nikita Simonov
Abstract
We consider Gagliardo–Nirenberg inequalities on the sphere which interpolate between the Poincaré inequality and the Sobolev inequality, and include the logarithmic Sobolev inequality as a special case. We establish explicit stability results in the subcritical regime using spectral decomposition techniques, and entropy and carré du champ methods applied to nonlinear diffusion flows.
Topics & Concepts
MathematicsLogarithmInterpolation (computer graphics)ConstructiveSobolev inequalityInequalitySobolev spaceStability (learning theory)Pure mathematicsApplied mathematicsMathematical analysisCalculus (dental)Computer scienceArtificial intelligenceMedicineDentistryOperating systemProcess (computing)Machine learningMotion (physics)Nonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringDifferential Equations and Boundary Problems