Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle

Scott Armstrong, Boyan Sirakov

Research output: Contribution to journalArticle

Abstract

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
Volume36
Issue number11
DOIs
StatePublished - Nov 2011

Fingerprint

Supersolution
Maximum principle
Maximum Principle
Elliptic Equations
Nonexistence
Cones
Quasilinear System
Exterior Domain
Fully Nonlinear
Nonlinear Operator
P-Laplacian
Unbounded Domain
Operator
Nonlinear Function
Simplicity
Cone
Robustness

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle. / Armstrong, Scott; Sirakov, Boyan.

In: Communications in Partial Differential Equations, Vol. 36, No. 11, 11.2011, p. 2011-2047.

Research output: Contribution to journalArticle

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