A temperature control problem (Q1061928)

This is a continuation of the work by the author [Regularity of the solution of an evolution problem with inequalities on the boundary, Commun. Partial Differ. Equations 7, 1453-1456 (1982)], where the regularity of the solution of a temperature control type free boundary problem was considered. In this paper the free boundary was proved to be a graph under a natural monotonicity condition. Moreover, in two dimensional space, the time derivative of the temperature is proved to be continuous across the free boundary.