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Stability Results for Sobolev, Logarithmic Sobolev, and Related Inequalities

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Obtaining explicit stability estimates in classical functional inequalities like the Sobolev inequality has been an essentially open question for 30 years, after the celebrated but non-constructive result of G. Bianchi and H. Egnell in 1991. Recently, new methods have emerged which provide some clues on these fascinating questions.
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