The boundary behavior and uniqueness of solutions of the heat equation.

Initial and relative limiting behaviour of temperatures on a strip

“…We are thus able to prove some new domination, non-negativity, uniqueness and representation theorems for temperatures. These results include a multi-variable version of a theorem of Gehring [6,Theorem 10], analogues of results for harmonic functions on a disc in the plane due to Bruckner, Lohwater and Ryan [4, Theorems 2 and 3], Hall [8,Theorem 4], and Lohwater [12], and a much more general version of a recent improvement for temperatures [15,Theorem 5] of a result of Krzyzanski [11,Theorem 5].…”