Subelliptic $p$-Laplacian spectral problem for Hörmander vector fields
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915422251515904 |
|---|---|
| author | Karazym, Mukhtar Suragan, Durvudkhan |
| author_facet | Karazym, Mukhtar Suragan, Durvudkhan |
| contents | Based on variational methods, we study the spectral problem for the subelliptic $p$-Laplacian arising from smooth Hörmander vector fields. We derive the smallest eigenvalue, prove its simplicity and isolatedness, establish the positivity of the first eigenfunction and show Hölder regularity of eigenfunctions. Moreover, we determine the best constant for the $L^{p}$-Poincaré-Friedrichs inequality for Hörmander vector fields as a byproduct. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14829 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Subelliptic $p$-Laplacian spectral problem for Hörmander vector fields Karazym, Mukhtar Suragan, Durvudkhan Analysis of PDEs 35P30, 35H20, 35J92, 35R03 Based on variational methods, we study the spectral problem for the subelliptic $p$-Laplacian arising from smooth Hörmander vector fields. We derive the smallest eigenvalue, prove its simplicity and isolatedness, establish the positivity of the first eigenfunction and show Hölder regularity of eigenfunctions. Moreover, we determine the best constant for the $L^{p}$-Poincaré-Friedrichs inequality for Hörmander vector fields as a byproduct. |
| title | Subelliptic $p$-Laplacian spectral problem for Hörmander vector fields |
| topic | Analysis of PDEs 35P30, 35H20, 35J92, 35R03 |
| url | https://arxiv.org/abs/2306.14829 |