Mathematical Research Letters

Volume 13, Issue 3, May 2006 pp. 441-453.

Decay at infinity of caloric functions within characteristic hyperplanes

Authors: L. Escauriaza (1), C.E. Kenig (2), G. Ponce (3), and L. Vega (4)
Author institution: Universidad del País Vasco (1), University of Chicago (2), University of California, Santa Barbara (3), and Universidad del País Vasco (4)

Summary: 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 $\linR^n\times [0,T]$.

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