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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2019-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/35/abstr.html |
| _version_ | 1818889066236608512 |
|---|---|
| author | Thomas Bieske Robert D. Freeman |
| author_facet | Thomas Bieske Robert D. Freeman |
| author_sort | Thomas Bieske |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-19T17:03:06Z |
| format | Article |
| id | doaj.art-8d00deab8e3a4cd9addb3647f3cd2054 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-19T17:03:06Z |
| publishDate | 2019-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-8d00deab8e3a4cd9addb3647f3cd20542022-12-21T20:13:15ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912019-02-01201935,113The p-Laplace equation in a class of Hormander vector fieldsThomas Bieske0Robert D. Freeman1 Univ. of South Florida, Tampa, FL, USA Univ. of South Florida, Tampa, FL, USA 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.http://ejde.math.txstate.edu/Volumes/2019/35/abstr.htmlp-LaplacianHormander vector fieldsfundamental solutionnonlinear potential theory |
| spellingShingle | Thomas Bieske Robert D. Freeman The p-Laplace equation in a class of Hormander vector fields Electronic Journal of Differential Equations p-Laplacian Hormander vector fields fundamental solution nonlinear potential theory |
| title | The p-Laplace equation in a class of Hormander vector fields |
| title_full | The p-Laplace equation in a class of Hormander vector fields |
| title_fullStr | The p-Laplace equation in a class of Hormander vector fields |
| title_full_unstemmed | The p-Laplace equation in a class of Hormander vector fields |
| title_short | The p-Laplace equation in a class of Hormander vector fields |
| title_sort | p laplace equation in a class of hormander vector fields |
| topic | p-Laplacian Hormander vector fields fundamental solution nonlinear potential theory |
| url | http://ejde.math.txstate.edu/Volumes/2019/35/abstr.html |
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