| Autor: |
Bonfiglioli, Andrea, Kogoj, Alessia E. |
| Rok vydání: |
2015 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We prove weighted $L^p$-Liouville theorems for a class of second order hypoelliptic partial differential operators $\mathcal{L}$ on Lie groups $\mathbb{G}$ whose underlying manifold is $n$-dimensional space. We show that a natural weight is the right-invariant measure $\check{H}$ of $\mathbb{G}$. We also prove Liouville-type theorems for $C^2$ subsolutions in $L^p(\mathbb{G},\check{H})$. We provide examples of operators to which our results apply, jointly with an application to the uniqueness for the Cauchy problem for the evolution operator $\mathcal{L}-\partial_t$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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