An Aronson-Bénilan / Li-Yau estimate in the JKO scheme in small dimension
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918436277321728 |
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| author | Coudreuse, Fanch |
| author_facet | Coudreuse, Fanch |
| contents | We derive an Aronson-Bénilan / Li-Yau estimate in the JKO scheme associated to the porous-medium, heat, and fast-diffusion equations, in dimensions $1$ and $2$, and on simple domains (cubes, quarter-space, half-spaces, whole space, and the torus). Our method is based on a maximum principle for the determinant of the Hessian of Brenier potentials, iterated as a one-step improvement along the scheme. As a consequence, we obtain local $L^\infty$ bounds on the density, uniform in the time step, consistent with the continuous-time result. As a byproduct, we rigorously derive the optimality conditions in the fast-diffusion case, filling a gap in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04169 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Aronson-Bénilan / Li-Yau estimate in the JKO scheme in small dimension Coudreuse, Fanch Analysis of PDEs Optimization and Control We derive an Aronson-Bénilan / Li-Yau estimate in the JKO scheme associated to the porous-medium, heat, and fast-diffusion equations, in dimensions $1$ and $2$, and on simple domains (cubes, quarter-space, half-spaces, whole space, and the torus). Our method is based on a maximum principle for the determinant of the Hessian of Brenier potentials, iterated as a one-step improvement along the scheme. As a consequence, we obtain local $L^\infty$ bounds on the density, uniform in the time step, consistent with the continuous-time result. As a byproduct, we rigorously derive the optimality conditions in the fast-diffusion case, filling a gap in the literature. |
| title | An Aronson-Bénilan / Li-Yau estimate in the JKO scheme in small dimension |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2604.04169 |