Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
A Selection Principle fo r the Sharp Quantitative Isoperimetric Inequality
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Existence of self-similar finite-mass solutions is proved for the time-fractional porous-medium equation in the optimal range m > (d-2)_+/d for all d ≥ 1, with compact support for m > 1 and heavy tails for m_c < m < 1.
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.
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Propagation of chaos for the Boltzmann equation with very soft potentials
Empirical measures from Kac's particle system converge to the Boltzmann equation solution for very soft potentials, proving propagation of chaos for all kernel classes.
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Self-similar solutions to the time-fractional Porous-Medium Equation
Existence of self-similar finite-mass solutions is proved for the time-fractional porous-medium equation in the optimal range m > (d-2)_+/d for all d ≥ 1, with compact support for m > 1 and heavy tails for m_c < m < 1.
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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.