Optimal Three Cylinder Inequality at the Boundary for Solutions to Parabolic Equations and Unique Continuation Properties |
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摘 要: |
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关 键 词: | 唯一连续 双曲线方程 稳定性估计 可测实函数 偏微分 |
收稿时间: | 10 November 2003 |
Optimal Three Cylinder Inequality at the Boundary for Solutions
to Parabolic Equations and Unique Continuation Properties |
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Authors: | Sergio Vessella |
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Institution: | (1) DiMaD, via Lombroso 6/17, 50134 Firenze, Italy |
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Abstract: | Let Γ be a portion of a C
1,α boundary of an n-dimensional domain D. Let u be a solution
to a second order parabolic equation in D × (–T, T) and assume that u = 0 on Γ × (–T, T), 0 ∈ Γ. We
prove that u satis.es a three cylinder inequality near Γ × (–T, T) . As a consequence of the previous
result we prove that if u (x, t) = O (|x|k) for every t ∈ (–T, T) and every k ∈ ℕ, then u is identically
equal to zero.
This work is partially supported by MURST, Grant No. MM01111258 |
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Keywords: | Unique continuation Parabolic equations Stability estimates |
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