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 |
| State | Published - Jun 1998 |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
A strong maximum principle for weak solutions of quasi-linear elliptic equations with applications to Lorentzian and Riemannian geometry. / Andersson, Lars; Galloway, Gregory J; Howard, Ralph.
In: Communications on Pure and Applied Mathematics, Vol. 51, No. 6, 06.1998, p. 581-624.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A strong maximum principle for weak solutions of quasi-linear elliptic equations with applications to Lorentzian and Riemannian geometry
AU - Andersson, Lars
AU - Galloway, Gregory J
AU - Howard, Ralph
PY - 1998/6
Y1 - 1998/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0032397328&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0032397328&partnerID=8YFLogxK
M3 - Article
VL - 51
SP - 581
EP - 624
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
SN - 0010-3640
IS - 6
ER -