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arXiv · 2206.12387

Holder estimates for kinetic Fokker-Planck equations up to the boundary

Luis Silvestre
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Abstract

We obtain local Holder continuity estimates up to the boundary for a kinetic Fokker-Planck equation with rough coefficients, with the prescribed influx boundary condition. Our result extends some recent developments that incorporate De Giorgi methods to kinetic Fokker-Planck equations. We also obtain higher order asymptotic estimates near the incoming part of the boundary. In particular, when the equation has a zero boundary conditions and no source term, we prove that the solution vanishes at infinite order on the incoming part of the boundary.

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Luis Silvestre. 2022-06-24. Holder estimates for kinetic Fokker-Planck equations up to the boundary. https://arxiv.org/abs/2206.12387

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