• DOI:10.1090/S0894-0347-08-00606-1
Corpus ID: 15472459

Tug-of-war and the infinity Laplacian

@inproceedings{Peres2006TugofwarAT,
  title={Tug-of-war and the infinity Laplacian},
  author={Yuval Peres and O. Schramm and Scott Sheffield and David Bruce Wilson},
  year={2006}
}

Yuval Peres, O. Schramm, +1 author David Bruce Wilson

Published 2006

Mathematics

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 for which Lip_U u = Lip_{boundary of U} u for all open subsets U of X that do not intersect Y. This was previously known only for bounded domains R^n, in which case u is infinity harmonic, that is, a viscosity solution to Delta_infty u = 0. We also prove the first general uniqueness results for Delta_infty u = g on bounded subsets of R^n (when… CONTINUE READING

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