Some comparison, symmetry and monotonicity results for Carnot-Carathéodory spaces (Q5954455)
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scientific article; zbMATH DE number 1700762
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some comparison, symmetry and monotonicity results for Carnot-Carathéodory spaces |
scientific article; zbMATH DE number 1700762 |
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Some comparison, symmetry and monotonicity results for Carnot-Carathéodory spaces (English)
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4 February 2002
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Carnot-Carathéodory metric space
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comparison results
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differential inequalities
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symmetry
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monotonicity
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0.93374944
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0.86916625
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0.8685825
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0.8684199
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0.8675117
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0.8639485
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0.86329454
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0.8630857
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The authors consider some nonlinear partial differential operators arising from a family of vector fields which define a Carnot-Carathéodory metric space. The authors prove some weak and strong comparison results for the related differential inequalities. These results are then used to prove some symmetry and monotonicity results for the corresponding solutions.NEWLINENEWLINENEWLINEThe references used in Sections 1 and 2 of the paper seem a little inaccurate and the authors seem to ignore the previous work of Saloff-Coste and Biroli-Mosco concerning Sobolev inequalities, cut-off functions on balls and the Harnack inequality [\textit{L. Saloff-Coste}, Potential Anal. 4, 429-468 (1995; Zbl 0840.31006); \textit{M. Biroli} and \textit{U. Mosco}, Potential Anal. 4, 311-324 (1995; Zbl 0833.46020) and Ann. Mat. Pura Appl. 169(4), 125-181 (1995; Zbl 0851.31008)].
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