{"ID":2857489,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.09231","arxiv_id":"2510.09231","title":"Li-Yau-Hamilton Inequality on the JKO Scheme for the Granular-Medium Equation","abstract":"We establish a version of the Li--Yau--Hamilton inequality for the Granular-Medium equation on the torus, both at the PDE level and for its time-discrete approximation given by the JKO scheme. We then apply this estimate to derive further quantitative results for the continuous and discrete JKO flows, including Lipschitz and $L^\\infty$ bounds, as well as a quantitative Harnack inequality. Finally, we use the regularity provided by this estimate to show that the JKO scheme for the Fokker--Planck equation converges in $L^2_{\\mathrm{loc}}((0,+\\infty); H^2(\\mathbb{T}^d))$.","short_abstract":"We establish a version of the Li--Yau--Hamilton inequality for the Granular-Medium equation on the torus, both at the PDE level and for its time-discrete approximation given by the JKO scheme. We then apply this estimate to derive further quantitative results for the continuous and discrete JKO flows, including Lipschi...","url_abs":"https://arxiv.org/abs/2510.09231","url_pdf":"https://arxiv.org/pdf/2510.09231v1","authors":"[\"Fanch Coudreuse\"]","published":"2025-10-10T10:18:49Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.OC\"]","methods":"[]","has_code":false}