A sub-Riemannian maximum principle and its application to the \(p\)-Laplacian in Carnot groups (Q2908735)
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scientific article; zbMATH DE number 6077169
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sub-Riemannian maximum principle and its application to the \(p\)-Laplacian in Carnot groups |
scientific article; zbMATH DE number 6077169 |
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5 September 2012
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sub-Riemannian geometry
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non-linear potential theory
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vicosity solutions
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\(p\)-Laplacian
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A sub-Riemannian maximum principle and its application to the \(p\)-Laplacian in Carnot groups (English)
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The author proves a sub-Riemannian maximum principle for semicontinuous functions and apply this principle to Carnot groups to provide a sub-Riemannian proof of the uniqueness of viscosity infinite harmonic functions. He also proves the equivalence of weak solutions and viscosity to the \(p\)-Laplace equation. We have to remark that this result extends the author's previous work in the Heisenberg group [Commun. Partial Differ. Equations 27, No. 3--4, 727--761 (2002; Zbl 1090.35063); Ann. Acad. Sci. Fenn., Math. 31, No. 2, 363--379 (2006; Zbl 1101.43003)].
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