The one-phase Stefan problem and the porous medium diffusion equation: Continuity of the solution in n space dimensions
Luis A. Caffarelli, Avner Friedman · Proceedings of the National Academy of Sciences · 1978
THE FOLLOWING PROBLEMS ARE CONSIDERED: (i) the one-phase Stefan problem, which describes the melting of ice, and (ii) the flow of gas in a porous medium. Both problems are considered in the n-dimensional space. The main result asserts that the solution [i.e., the temperature in problem (i) and the density in problem (ii)] is continuous.