Anisotropic Maximal $L^p$-regularity Estimates for a Hypoelliptic Operator
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910026979868672 |
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| author | Hirao, Kazuhiro |
| author_facet | Hirao, Kazuhiro |
| contents | We consider the maximal regularity of a specific Vlasov-Fokker-Planck equation $\mathcal{A}u=f$ in the Euclidean space. The operator $\mathcal{A}=Δ_{y}u-y\cdot \nabla_x{u}$ is an example of the Ornstein-Uhlenbeck operators. We prove the existence of a solution that satisfies the anisotropic maximal regularity estimates. To prove this we also show a similar estimates and a weak (1, 1) estimate for $L=\partial_t-\mathcal{A}$, which is of independent interest. These results rely on the pointwise estimates of the fundamental solution of $L$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17378 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Anisotropic Maximal $L^p$-regularity Estimates for a Hypoelliptic Operator Hirao, Kazuhiro Analysis of PDEs 35H10 (Primary) 35B65, 42B20, 35B30 (Secondary) We consider the maximal regularity of a specific Vlasov-Fokker-Planck equation $\mathcal{A}u=f$ in the Euclidean space. The operator $\mathcal{A}=Δ_{y}u-y\cdot \nabla_x{u}$ is an example of the Ornstein-Uhlenbeck operators. We prove the existence of a solution that satisfies the anisotropic maximal regularity estimates. To prove this we also show a similar estimates and a weak (1, 1) estimate for $L=\partial_t-\mathcal{A}$, which is of independent interest. These results rely on the pointwise estimates of the fundamental solution of $L$. |
| title | Anisotropic Maximal $L^p$-regularity Estimates for a Hypoelliptic Operator |
| topic | Analysis of PDEs 35H10 (Primary) 35B65, 42B20, 35B30 (Secondary) |
| url | https://arxiv.org/abs/2602.17378 |