Variational and Perron–Wiener solutions in stratified Lie groups |
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Authors: | Beatrice Abbondanza |
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Institution: | Dipartimento di Matematica, Università di Bologna, Bologna, Italy |
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Abstract: | We consider sub‐Laplacians in stratified Lie groups and we compare Perron–Wiener and weak‐variational solutions of the Dirichlet problem , where Ω is a bounded open set in and φ is the restriction to the boundary of a function such that . The result we obtained extends a previous theorem by Arendt and Daners, related to the classial Laplacian in . |
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Keywords: | Dirichlet's problem weak solution Perron– Wiener solution sub‐Laplacian on Carnot groups 31B05 35D30 35D99 35J25 35R03 |
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