Mathematical Research Letters

Volume 13 (2006)

Number 3

Decay at infinity of caloric functions within characteristic hyperplanes

Pages: 441 – 453

DOI: http://dx.doi.org/10.4310/MRL.2006.v13.n3.a8

Authors

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)

Abstract

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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