Sharp gradient stability for the Sobolev inequality
Alessio Figalli, Yi Ru‐Ya Zhang
Abstract
We prove a sharp quantitative version of the p-Sobolev inequality for any 1<p<n, with a control on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent is constant for p≤2, while it depends on p for p>2.
Topics & Concepts
MathematicsSobolev spaceExponentSobolev inequalityConstant (computer programming)Class (philosophy)InequalityStability (learning theory)Mathematical analysisPure mathematicsLinguisticsProgramming languageMachine learningPhilosophyArtificial intelligenceComputer scienceNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problems