The Euler Equation and¶Absolute Minimizers of L∞ Functionals

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.