A domain monotonicity property of the Neumann heat kernel
Elton P. Hsu · Osaka City University (Osaka City University) · 1994
Physically pa{ty x, y) represents the temperautre distribution in Ω at time t and point y if a heat source of total capacity one is present at point x at time 0 with the assumption that the boundary 9Ω is impervious to heat conduction (adiabatic boundary). From this interpretation of the Neumann heat kernel it was conjectured (see Chavel [2] and Kendall [7]) that if Ω is a smooth convex domain and D is another smooth domain containing Ω, then for all (ΐy xy y) e (0, oo)χΩχΩ