The Euler Equation and¶Absolute Minimizers of L∞ Functionals

By E. Barron, R. Jensen, Changyou Wang. 2001

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Principles of comparison with distance functions for absolute minimizers (2007, background): “1) holds under mild assumptions, see [3, 4, 9].”
The Aronsson equation for absolute minimizers of ${L^\infty}$-functionals associated with vector fields satisfying Hörmander's condition (2003, methodology): “ §2. Proof of theorem A This section is devoted to the proof of theorem A. It contains two steps: (i) the construction of test functions by solving the Hamilton-Jacobi equation, which is motivated by [BJW] and [C]; (ii) the comparison between viscosity subsolution and classical strict supersolution ”
A TOUR OF THE THEORY OF ABSOLUTELY MINIMIZING FUNCTIONS (2004, background): “However, as far as we know, there are no existence results for absolute minimizers in the vector-valued case except when X = R, which is treated by Barron, Jensen and Wang [13].”
A Visit with the ∞-Laplace Equation (2008, methodology): “It was shown by Barron, Jensen and Wang [11] that if u is absolutely minimizing for F ∞, then A[u] = 0 in the viscosity sense.”
Generalised Solutions for Fully Nonlinear PDE Systems and Existence-Uniqueness Theorems (2015, unknown): “For instance, the deep contributions [BJW1, BJW2] essentially aimed at studying only the functional when N ≥ 2.”