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On global solutions to semilinear elliptic equations related to the one-phase free boundary problem
Motivated by its relation to models of flame propagation, we study globally Lipschitz solutions of $ \Delta u = f(u) $ in $ \mathbb{R}^n $, where $ f $ is smooth, non-negative, with support in the interval $ [0,1] $. In such setting, any 'blow-down' of the solution $ u …