The p-Laplace equation in a class of Hörmander vector fields
| dc.contributor.author | Bieske, Thomas | |
| dc.contributor.author | Freeman, Robert D. | |
| dc.date.accessioned | 2021-11-01T17:47:51Z | |
| dc.date.available | 2021-11-01T17:47:51Z | |
| dc.date.issued | 2019-02-28 | |
| dc.description.abstract | We find the fundamental solution to the p-Laplace equation in a class of Hormander vector fields that generate neither a Carnot group nor a Grushin-type space. The singularity occurs at the sub-Riemannian points, which naturally corresponds to finding the fundamental solution of a generalized operator in Euclidean space. We then extend these solutions to a generalization of the p-Laplace equation and use these solutions to find infinite harmonic functions and their generalizations. We also compute the capacity of annuli centered at the singularity. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 13 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Bieske, T., & Freeman, R. D. (2019). The p-Laplace equation in a class of Hörmander vector fields. <i>Electronic Journal of Differential Equations, 2019</i>(35), pp. 1-13. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14744 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | p-Laplacian | |
| dc.subject | Hörmander vector fields | |
| dc.subject | Fundamental solution | |
| dc.subject | Nonlinear potential theory | |
| dc.title | The p-Laplace equation in a class of Hörmander vector fields | |
| dc.type | Article |