The p-Laplace equation in a class of Hormander vector fields
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 op...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2019-02-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/35/abstr.html |
| Summary: | 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. |
|---|---|
| ISSN: | 1072-6691 |