Boundary regularity for subelliptic equations in the Heisenberg group
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909639532085248 |
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| author | Abedin, Farhan Tralli, Giulio |
| author_facet | Abedin, Farhan Tralli, Giulio |
| contents | We prove boundary Hölder and Lipschitz regularity for a class of degenerate elliptic, second order, inhomogeneous equations in non-divergence form structured on the left-invariant vector fields of the Heisenberg group. Our focus is on the case of operators with bounded and measurable coefficients and bounded right-hand side; when necessary, we impose a dimensional restriction on the ellipticity ratio and a growth rate for the source term near characteristic points of the boundary. For solutions in the characteristic half-space $\{t>0\}$, we obtain an intrinsic second order expansion near the origin when the source term belongs to an appropriate weighted $L^{\infty}$ space; this is a new result even for the frequently studied sub-Laplacian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05151 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary regularity for subelliptic equations in the Heisenberg group Abedin, Farhan Tralli, Giulio Analysis of PDEs 35J70, 35R05, 35H20, 35B45 We prove boundary Hölder and Lipschitz regularity for a class of degenerate elliptic, second order, inhomogeneous equations in non-divergence form structured on the left-invariant vector fields of the Heisenberg group. Our focus is on the case of operators with bounded and measurable coefficients and bounded right-hand side; when necessary, we impose a dimensional restriction on the ellipticity ratio and a growth rate for the source term near characteristic points of the boundary. For solutions in the characteristic half-space $\{t>0\}$, we obtain an intrinsic second order expansion near the origin when the source term belongs to an appropriate weighted $L^{\infty}$ space; this is a new result even for the frequently studied sub-Laplacian. |
| title | Boundary regularity for subelliptic equations in the Heisenberg group |
| topic | Analysis of PDEs 35J70, 35R05, 35H20, 35B45 |
| url | https://arxiv.org/abs/2506.05151 |