Liouville-type theorems for real sub-Laplacians |
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Authors: | Andrea Bonfiglioli Ermanno Lanconelli |
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Institution: | Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna, Italia.?e-mail: bonfigli@dm.unibo.it; lanconel@dm.unibo.it, IT
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Abstract: | An inequality generalizing the classical Liouville and Harnack Theorems for real sub-Laplacians ℒ is proved. A representation
formula for functions $u$ for which ℒu is a polynomial is also showed. As a consequence, some conditions are given ensuring that u is a polynomial whenever ℒu is a polynomial. Finally, an application of this last result is given: if ψ is a C
2 map commuting with ℒ, then any of its component is a polynomial function.
Received: 3 November 2000 |
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Keywords: | Mathematics Subject Classification (2000): 35H20 35B05 35J70 43A80 |
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