Geodesic
Holder estimates for kinetic Fokker-Planck equations up to the boundary
Ars Inveniendi Analytica (2022)

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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.
Publié le :
DOI : 10.15781/nqdd-qs03 
@article{10_15781_nqdd_qs03,
     author = {Luis Silvestre},
     title = {Holder estimates for kinetic {Fokker-Planck} equations up to the boundary},
     journal = {Ars Inveniendi Analytica},
     publisher = {mathdoc},
     year = {2022},
     doi = {10.15781/nqdd-qs03},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.15781/nqdd-qs03/}
}
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Luis Silvestre. Holder estimates for kinetic Fokker-Planck equations up to the boundary. Ars Inveniendi Analytica (2022). doi: 10.15781/nqdd-qs03

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