# 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} }

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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