Decay at infinity of caloric functions within characteristic hyperplanes

L. Escauriaza; C. E. Kenig; G. Ponce; L. Vega

Decay at infinity of caloric functions within characteristic hyperplanes

Analysis of PDEs 2007-05-23 v1

Authors: L. Escauriaza , C. E. Kenig , G. Ponce , L. Vega

Abstract

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

Cite

@article{arxiv.math/0509436,
  title  = {Decay at infinity of caloric functions within characteristic hyperplanes},
  author = {L. Escauriaza and C. E. Kenig and G. Ponce and L. Vega},
  journal= {arXiv preprint arXiv:math/0509436},
  year   = {2007}
}

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