Initial traces of solutions to a one-phase Stefan problem in an infinite strip.
The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u ∈ L1loc (Rn x (0,T)) to(0.1) ut - Δ(u - 1)+ = 0, in D'(Rn x (0,T)),for T > 0, n ≥ 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection u is the enthalpy, (u - 1)+ the temperature, and u = 1 the critical temperature of change of phase. Our estimate may be written in the form(0.2) ∫Rn u(x,t) e-|x|2 / (2 (T - t)) dx ≤ C, 0 <...