Convexity Criteria and Uniqueness of Absolutely Minimizing Functions

Scott N. Armstrong, Michael G. Crandall, Vesa Julin, Charles K. Smart

Research output: Contribution to journalArticle

Abstract

We show that an absolutely minimizing function with respect to a convex Hamiltonian H:ℝn→ ℝis uniquely determined by its boundary values under minimal assumptions on H. Along the way, we extend the known equivalences between comparison with cones, convexity criteria, and absolutely minimizing properties, to this generality. These results perfect a long development in the uniqueness/existence theory of the archetypal problem of the calculus of variations in L.

Original languageEnglish (US)
Pages (from-to)405-443
Number of pages39
JournalArchive for Rational Mechanics and Analysis
Volume200
Issue number2
DOIs
StatePublished - May 2011

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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