Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle

Scott N. Armstrong, Boyan Sirakov

Research output: Contribution to journalArticlepeer-review


We introduce a new method for proving the nonexistence of positive supersolutions of elliptic inequalities in unbounded domains of ℝ n. The simplicity and robustness of our maximum principle-based argument provides for its applicability to many elliptic inequalities and systems, including quasilinear operators such as the p-Laplacian, and nondivergence form fully nonlinear operators such as Bellman-Isaacs operators. Our method gives new and optimal results in terms of the nonlinear functions appearing in the inequalities, and applies to inequalities holding in the whole space as well as exterior domains and cone-like domains.

Original languageEnglish (US)
Pages (from-to)2011-2047
Number of pages37
JournalCommunications in Partial Differential Equations
Issue number11
StatePublished - Nov 2011


  • Fully nonlinear equation
  • Lane-Emden system
  • Liouville theorem
  • Semilinear equation
  • p-Laplace equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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