Properties of harmonic measures in the Dirichlet problem for nilpotent lie groups of Heisenberg type

Luca Capogna, Nicola Garofalo, Duy Minh Nhieu

研究成果: 雜誌貢獻期刊論文同行評審

19 引文 斯高帕斯(Scopus)

摘要

In groups of Heisenberg type we introduce a large class of domains, which we call ADP, admissible for the Dirichlet problem, and we prove that on the boundary of such domains, harmonic measure, ordinary surface measure, and the perimeter measure, are mutually absolutely continuous. We also establish the solvability of the Dirichlet problem when the boundary datum belongs to LP, 1 < p ≤ ∞, with respect to the ordinary surface measure. Here, the harmonic measure is that relative to a sub-Laplacian associated with a basis of the first layer of the Lie algebra. A domain is called ADP if it is a nontangentially accessible domain and it satisfies an intrinsic outer ball condition.

原文???core.languages.en_GB???
頁(從 - 到)273-306
頁數34
期刊American Journal of Mathematics
124
發行號2
DOIs
出版狀態已出版 - 2002

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