Archive for Rational Mechanics and Analysis

, Volume 157, Issue 4, pp 255–283

The Euler Equation and¶Absolute Minimizers of L∞ Functionals

Authors

  • E. N. Barron
    • Loyola University Chicago¶Department of Mathematical Sciences¶Chicago, IL 60626¶e-mail: enb@math.luc.edu, rrj@math.luc.edu
  • R. R. Jensen
    • Loyola University Chicago¶Department of Mathematical Sciences¶Chicago, IL 60626¶e-mail: enb@math.luc.edu, rrj@math.luc.edu
  • C. Y. Wang
    • University of Kentucky¶Department of Mathematics¶Lexington, KY 40506¶e-mail: cywang@ms.uky.edu

DOI: 10.1007/PL00004239

Cite this article as:
Barron, E., Jensen, R. & Wang, C. Arch. Rational Mech. Anal. (2001) 157: 255. doi:10.1007/PL00004239

Abstract:

The Aronsson-Euler equation for the functional
$$$$
on Wg1, ∞(Ω, ℝm, i.e., W1, ∞ with boundary data g, is
$$$$

This equation has been derived for smooth absolute minimizers, i.e., a function which minimizes F on every subdomain. We prove in this paper that for m=1, n≧ 1, or n=1, m≧ 1 an absolute minimizer of F exists in Wg1, ∞(Ω, ℝm and for m= 1, n≧ 1 any absolute minimizer of F must be a viscosity solution of the Aronsson-Euler equation.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001