A strong maximum principle for weak solutions of quasi-linear elliptic equations with applications to Lorentzian and Riemannian geometry

Lars Andersson, Gregory J Galloway, Ralph Howard

Research output: Contribution to journalArticle

15 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)581-624
Number of pages44
JournalCommunications on Pure and Applied Mathematics
Volume51
Issue number6
StatePublished - Jun 1998

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Lorentzian Geometry
Strong Maximum Principle
Sub- and Supersolutions
Spacelike Hypersurface
Lorentzian Manifolds
Warped Product
Support Function
Riemannian geometry
Maximum principle
Quasilinear Elliptic Equation
Mean Curvature
Weak Solution
Geometry
Theorem
Class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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