### 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 C^{0}-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 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*51*(6), 581-624.

**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.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 51, no. 6, pp. 581-624.

}

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 -