Singular Solutions of Fully Nonlinear Elliptic Equations and Applications

Scott N. Armstrong, Boyan Sirakov, Charles K. Smart

Research output: Contribution to journalArticle

Abstract

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of ℝ n, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragmén-Lindelöf result as well as a principle of positive singularities in certain Lipschitz domains.

Original languageEnglish (US)
Pages (from-to)345-394
Number of pages50
JournalArchive for Rational Mechanics and Analysis
Volume205
Issue number2
DOIs
StatePublished - Aug 2012

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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