Two-Phase Stefan Problems. Recent Results and Open Questions

Existence and Boundary Regularity for Degenerate Phase Transitions

“…In this paper we complete the tour de force, initiated in [1], concerning the regularity of weak solutions for the degenerate (p ≥ 2) two-phase Stefan problem [13,14]  …”

A Quantitative Modulus of Continuity for the Two-Phase Stefan Problem

“…We mention that the model (1.4) also finds applications in finance [25], biology related to the Lotka-Volterra model [6], and flows of solutes or gases in porous media [26]. Clearly (1.4) and (1.1) need to be understood using an appropriate notion of (weak) solution, and the one we employ is that of differential inclusion in the sense of graphs, see Definition 1.9; other approaches can be used and the most noticeable one is that of viscosity solutions in the sense introduced by Crandall and Lions, and developed by Caffarelli; see [2] and the recent survey by Salsa [28]. Notice that weak solutions are viscosity solutions once one knows they are continuous (and in fact they are, see the following lines); under an additional conditions (namely, {u = 0} is negligible) the converse also holds true, see [19].…”

On the classical solutions of the three dimensional Stefan problem

“…In this paper the author proves the existence and uniqueness of a generalized solution for the three-dimensional Stefan problem, later improved by her master Olga Oleinik. Salsa [9], on the other hand, suggested recent results and open problems of the Stefan problem. According to [9],…”

“…Salsa [9], on the other hand, suggested recent results and open problems of the Stefan problem. According to [9],…”