Mathematical Research Letters

Volume 13 (2006)

Number 3

Decay at infinity of caloric functions within characteristic hyperplanes

Pages: 441 – 453



L. Escauriaza (Universidad del País Vasco)

C. E. Kenig (University of Chicago)

G. Ponce (University of California at Santa Barbara)

L. Vega (Universidad del País Vasco)


It is shown that a function $u$ satisfying, $|\Delta u+\partial_tu|\le M\left(|u|+|\nabla u|\right)$, $|u(x,t)|\le Me^{M|x|^2}$ in $\linR^n\times [0,T]$ and $|u(x,0)|\le C_ke^{-k|x|^2}$ in $\linR^n$ for all $k\ge 1$, must vanish identically in $\linR^n\times [0,T]$.

Published 1 January 2006