On the exterior domain problem for one phase free boundary


We considered the asymptotic behavior of one-phase free boundary graph in one exterior domain. We obtained that the solution is Lipschitz continuous, non-degenerate, and has one specific version of Weiss's monotonicity formula by adding extra terms. In planar case, we proved the asymptotic flatness of the solution in some sense, and we also discussed higher dimensional cases under additional conditions.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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