2019 **Abstract:** We discuss two distinct minimality principles for general supremal first order functionals for maps and characterise them through solvability of associated second order PDE systems. Specifically, we consider Aronsson's standard notion of absolute minimisers and the concept of ∞-minimal maps introduced more recently by the second author. We prove that C 1 absolute minimisers characterise a divergence system with parameters probability measures and that C 2 ∞-minimal maps characterise Aronsson's PDE system. Sinc…

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“…In the vectorial case of N ≥ 2, the situation is trickier and the "correct" localised minimality notion is still under discussion, even without any constraints being involved (see e.g. [3,4] for work in this direction).…”

confidence: 99%

“…In the vectorial case of N ≥ 2, the situation is trickier and the "correct" localised minimality notion is still under discussion, even without any constraints being involved (see e.g. [3,4] for work in this direction).…”

confidence: 99%

“…Even in the unconstrained case, these PDE systems are always non-divergence and even fully nonlinear and with continuous coefficients (see e.g. [7,8,23,37,43]). The case of L ∞ problems involving only first order derivative of scalar-valued functions is nowadays a well established field which originated from the work of Aronsson in the 1960 [4,5], today largely interconnected to the theory of Viscosity Solution to nonlinear elliptic PDE (for a general pedagogical introduction see e.g.…”

confidence: 99%