ON RATIO INEQUALITIES FOR HEAT CONTENT
Burgess Davis, Majid Hosseini · Journal of the London Mathematical Society · 2004
Let U be a domain, convex in x and symmetric about the y-axis, which is contained in a centered and oriented rectangle S. It is proved that Ht(U+)/Ht(U)⩽Ht(S+)/Ht(S) where Ht stands for heat content, that is, the remaining heat in the domain at time t if it initially has uniform temperature 1, with Dirichlet boundary conditions, where A+=A∩{(x,y):x>0}. It is also shown that the analog of this inequality holds for some other Schrödinger operators.