Tug-of-war and the infinity Laplacian

نویسندگان

  • Yuval Peres
  • Oded Schramm
  • Scott Sheffield
  • David B. Wilson
چکیده

We prove that every bounded Lipschitz function F on a subset Y of a length space X admits a tautest extension to X, i.e., a unique Lipschitz extension u : X → R for which LipUu = Lip∂Uu for all open U ⊂ X r Y . This was previously known only for bounded domains in Rn, in which case u is infinity-harmonic, that is, a viscosity solution to ∆∞u = 0, where

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تاریخ انتشار 2005