, Volume 157, Issue 4, pp 255-283

The Euler Equation and¶Absolute Minimizers of L∞ Functionals

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Abstract:

The Aronsson-Euler equation for the functional on W g 1, ∞(Ω, ℝ m , i.e., W 1, ∞ 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 W g 1, ∞(Ω, ℝ m and for m= 1, n≧ 1 any absolute minimizer of F must be a viscosity solution of the Aronsson-Euler equation.

Accepted November 13, 2000¶Published online April 23, 2001