Decay at infinity of caloric functions within characteristic hyperplanes

2005/09/19 by Luis Escauriaza, L. Escauriaza, Escauriaza, L. +9
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.AP

paper · pdf · doi:10.48550/arxiv.math/0509436

arxiv created 2005/09/19 · openalex publication_date 2005/09/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that a function u satisfying, |Δu+∂_tu|≤ M(|u|+|∇ u|), |u(x,t)|≤ Me^M|x|2 in \Rⁿ× [0,T] and |u(x,0)|≤ C_ke^-k|x|2 in \Rⁿ and for all k≥ 1, must vanish identically in \Rⁿ× [0,T].

Citations

• On localization in the continuous Anderson-Bernoulli model in higher dimension

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