Abstract
The strong maximum principle is proved to hold for weak (in the sense of support functions) sub-and supersolutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for C0-space-like hypersurfaces in a Lorentzian manifold. As one application, a Lorentzian warped product splitting theorem is given.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 581-624 |
| Number of pages | 44 |
| Journal | Communications on Pure and Applied Mathematics |
| Volume | 51 |
| Issue number | 6 |
| DOIs | |
| State | Published - Jun 1998 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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Cite this
Andersson, L., Galloway, G. J., & Howard, R. (1998). A strong maximum principle for weak solutions of quasi-linear elliptic equations with applications to Lorentzian and Riemannian geometry. Communications on Pure and Applied Mathematics, 51(6), 581-624. https://doi.org/10.1002/(SICI)1097-0312(199806)51:6<581::AID-CPA2>3.0.CO;2-3