The Infinity Laplacian, Aronsson’s Equation and Their Generalizations
نویسندگان
چکیده
The infinity Laplace equation ∆∞u = 0 arose originally as a sort of Euler–Lagrange equation governing the absolute minimizer for the L∞ variational problem of minimizing the functional ess-supU |Du|. The more general functional ess-supUF (x, u, Du) leads similarly to the so-called Aronsson equation AF [u] = 0. In this paper we show that these PDE operators and various interesting generalizations also appear in several other contexts seemingly quite unrelated to L∞ variational problems, including two-person game theory with random order of play, rapid switching of states in control problems, etc. The resulting equations can be parabolic and inhomogeneous, equation types precluded in conventional L∞ variational problems.
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