For supremal functionals with Hessian and lower-order terms, the paper proves existence of minimizers, derives the third-order Aronsson-type PDE, and establishes generalized D-solutions.
Aronsson, Minimization problems for the functional supxF (x, f(x), f′(x))
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On Second-Order $L^\infty$ Variational Problems with Lower-Order Terms
For supremal functionals with Hessian and lower-order terms, the paper proves existence of minimizers, derives the third-order Aronsson-type PDE, and establishes generalized D-solutions.