Strong comparison principle for $p$-harmonic functions in Carnot-Caratheodory spaces
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- by Luca Capogna and Xiaodan Zhou PDF
- Proc. Amer. Math. Soc. 146 (2018), 4265-4274 Request permission
Abstract:
We extend Bony’s propagation of support argument to $C^1$ solutions of the nonhomogeneous subelliptic $p$-Laplacian associated to a system of smooth vector fields satisfying Hörmander’s finite rank condition. As a consequence we prove a strong maximum principle and strong comparison principle that generalize results of Tolksdorf.References
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Additional Information
- Luca Capogna
- Affiliation: Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, Massachusetts 01609
- MR Author ID: 336615
- Email: lcapogna@wpi.edu
- Xiaodan Zhou
- Affiliation: Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, Massachusetts 01609
- MR Author ID: 1150978
- Email: xzhou3@wpi.edu
- Received by editor(s): July 19, 2017
- Received by editor(s) in revised form: December 11, 2017
- Published electronically: July 13, 2018
- Additional Notes: The first author was partially funded by NSF awards DMS 1449143 and DMS 1503683.
The second author was partially funded by an AMS–Simons Travel Grant - Communicated by: Jeremy Tyson
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4265-4274
- MSC (2010): Primary 35H20, 35B50
- DOI: https://doi.org/10.1090/proc/14113
- MathSciNet review: 3834656