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Decay at infinity of caloric functions within characteristic hyperplanes

L. Escauriaza·C. E. Kenig·G. Ponce·L. Vega
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Abstract

It is shown that a function $u$ satisfying, $|Δu+\partial_tu|\le M(|u|+|\nabla u|)$, $|u(x,t)|\le Me^{M|x|^2}$ 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 $\R^n\times [0,T]$.

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L. Escauriaza, C. E. Kenig, G. Ponce, L. Vega. 2005-09-19. Decay at infinity of caloric functions within characteristic hyperplanes. https://arxiv.org/abs/math/0509436

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