Decay at infinity of caloric functions within characteristic hyperplanes

L. Escauriaza, C. E. Kenig, G. Ponce +1

It is shown that a function $u$ satisfying, $|\Delta u+{\partial }_{t}u|\le M(|u|+|\nabla u|)$, $|u(x,t)|\le M{e}^{M|x{|}^2}$ in ${\mathbb{R}}^n\times [0,T]$ and $|u(x,0)|\le C_k{e}^{-k|x{|}^2}$ in ${\mathbb{R}}^n$ and…