Stability with sharp exponent 2 holds for the L^p-Talenti inequality when f is the characteristic function of a subset of the unit ball.
Quantitative Stability fo r Eigenvalues of Schrödinger Operator, Quantitative Bathtub Principle, and Application to the Turnpike Property for a Bilinear Optimal Control Problem
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Sharp quantitative Talenti's inequality in particular cases
Stability with sharp exponent 2 holds for the L^p-Talenti inequality when f is the characteristic function of a subset of the unit ball.