The paper establishes an Aronson-Bénilan/Li-Yau estimate inside the JKO discretization of diffusion equations in low dimensions, giving time-step-uniform L^∞ density bounds via a maximum principle on the Hessian determinant of Brenier potentials.
The Variational Formulation of the Fokker–Planck Equation.SIAM Journal on Mathematical Analysis, 29(1):1–17
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An Aronson-B\'enilan / Li-Yau estimate in the JKO scheme in small dimension
The paper establishes an Aronson-Bénilan/Li-Yau estimate inside the JKO discretization of diffusion equations in low dimensions, giving time-step-uniform L^∞ density bounds via a maximum principle on the Hessian determinant of Brenier potentials.