The 𝑃-Laplace equation on a class of Grushin-type spaces
| Autor: | Thomas Bieske, Jasun Gong |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Computer Science::Machine Learning
Laplace's equation Euclidean space Applied Mathematics General Mathematics Weak solution Mathematical analysis MathematicsofComputing_GENERAL Computer Science::Digital Libraries Statistics::Machine Learning Singularity Harmonic function Computer Science::Mathematical Software Fundamental solution Method of fundamental solutions Laplace operator Mathematics |
| Zdroj: | Proceedings of the American Mathematical Society. 134:3585-3594 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/s0002-9939-06-08394-8 |
| Popis: | We find the fundamental solution to the P P -Laplace equation in Grushin-type spaces. The singularity occurs at the sub-Riemannian points, which naturally corresponds to finding the fundamental solution of a generalized Grushin operator in Euclidean space. We then use this solution to find an infinite harmonic function with specific boundary data and to compute the capacity of annuli centered at the singularity. A solution to the 2-Laplace equation in a wider class of spaces is presented. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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