Velocity Averaging and Hölder Regularity for Kinetic Fokker--Planck Equations with General Transport Operators and Rough Coefficients
| Autor: | Yuzhe Zhu |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Applied Mathematics
Mathematical analysis Mathematics::Analysis of PDEs Hölder condition 16. Peace & justice Kinetic energy 01 natural sciences 010101 applied mathematics 35B65 35H10 35Q84 Computational Mathematics Mathematics - Analysis of PDEs FOS: Mathematics Local boundedness Fokker–Planck equation 0101 mathematics Analysis Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | SIAM Journal on Mathematical Analysis. 53:2746-2775 |
| ISSN: | 1095-7154 0036-1410 |
| DOI: | 10.1137/20m1372147 |
| Popis: | This article addresses the local boundedness and H\"older continuity of weak solutions to kinetic Fokker-Planck equations with general transport operators and rough coefficients. These results are due to the mixing effect of diffusion and transport. Although the equation is parabolic only in the velocity variable, it has a hypoelliptic structure provided that the transport part $\partial_t+b(v)\cdot\nabla_x$ is nondegenerate in some sense. We achieve the results by revisiting the method, proposed by Golse, Imbert, Mouhot and Vasseur in the case $b(v)= v$, that combines the elliptic De Giorgi-Nash-Moser theory with velocity averaging lemmas. Comment: 28 pages |
| Databáze: | OpenAIRE |
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