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Variational and Perron–Wiener solutions in stratified Lie groups
Author(s) -
Abbondanza Beatrice
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400168
Subject(s) - mathematics , bounded function , open set , lie group , laplace operator , dirichlet distribution , boundary (topology) , pure mathematics , mathematical analysis , function (biology) , boundary value problem , evolutionary biology , biology
We consider sub‐Laplacians L in stratified Lie groups and we compare Perron–Wiener and weak‐variational solutions of the Dirichlet problem h ∈ H ( Ω ) ∩ C ( Ω ¯ ), h | ∂ Ω = φ , where Ω is a bounded open set in R N and φ is the restriction to the boundary of a function ϕ ∈ C ( Ω ¯ ) such that L ϕ ∈ H − 1( Ω ) . The result we obtained extends a previous theorem by Arendt and Daners, related to the classial Laplacian in R N .