Singular Solutions of Fully Nonlinear Elliptic Equations and Applications

Scott 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

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Fully Nonlinear Elliptic Equations
Lipschitz Domains
Singular Solutions
Boundary Singularities
Isolated Singularity
Fully Nonlinear
Behavior of Solutions
Elliptic Equations
Lipschitz
Positive Solution
Cone
Classify
Singularity
Cones

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

Singular Solutions of Fully Nonlinear Elliptic Equations and Applications. / Armstrong, Scott; Sirakov, Boyan; Smart, Charles K.

In: Archive for Rational Mechanics and Analysis, Vol. 205, No. 2, 08.2012, p. 345-394.

Research output: Contribution to journalArticle

Armstrong, Scott ; Sirakov, Boyan ; Smart, Charles K. / Singular Solutions of Fully Nonlinear Elliptic Equations and Applications. In: Archive for Rational Mechanics and Analysis. 2012 ; Vol. 205, No. 2. pp. 345-394.
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