Global $L^p$ estimate for some kind of Kolmogorov-Fokker-Planck Equations in nondivergence form
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914049958084608 |
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| author | Suo, Liyuan |
| author_facet | Suo, Liyuan |
| contents | In this paper, we mainly investigate a class of Kolmogorov-Fokker-Planck operator with 4 different scalings in nondivergence form. And we assume the coefficients $a^{ij}$ are only measurable in $t$ and satisfy the vanishing mean oscillation in space variables. We establish a global priori estimates of $\nabla_x^u$, $( -Δ_y )^{1/3} u$ and $( -Δ_z )^{1/5} u$ in $L^p$ space which extend the work of Dong and Yastrzhembskiy \cite{ref49} where they focus on the 3 different scalings KFP operator. Moreover we establish a kind of Poincare inequality for homogeneous equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17961 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global $L^p$ estimate for some kind of Kolmogorov-Fokker-Planck Equations in nondivergence form Suo, Liyuan Analysis of PDEs 35K70, 35H10, In this paper, we mainly investigate a class of Kolmogorov-Fokker-Planck operator with 4 different scalings in nondivergence form. And we assume the coefficients $a^{ij}$ are only measurable in $t$ and satisfy the vanishing mean oscillation in space variables. We establish a global priori estimates of $\nabla_x^u$, $( -Δ_y )^{1/3} u$ and $( -Δ_z )^{1/5} u$ in $L^p$ space which extend the work of Dong and Yastrzhembskiy \cite{ref49} where they focus on the 3 different scalings KFP operator. Moreover we establish a kind of Poincare inequality for homogeneous equations. |
| title | Global $L^p$ estimate for some kind of Kolmogorov-Fokker-Planck Equations in nondivergence form |
| topic | Analysis of PDEs 35K70, 35H10, |
| url | https://arxiv.org/abs/2405.17961 |