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arXiv · 1711.06730

Quantitative unique continuation for a parabolic equation

Guher Camliyurt·Igor Kukavica
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Abstract

We address the quantitative uniqueness properties of the solutions of the parabolic equation $ \partial_t u - \Delta u = w_j (x,t) \partial_j u + v(x,t) u $ where $v$ and $w$ are bounded. We prove that for solutions $u$, the order of vanishing is bounded by $C(\Vert v\Vert_{L^\infty}^{2/3}+\Vert w\Vert_{L^\infty}^2)$ matching the upper bound previously established in the elliptic case. in the elliptic case.

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Guher Camliyurt, Igor Kukavica. 2017-11-17. Quantitative unique continuation for a parabolic equation. https://arxiv.org/abs/1711.06730

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