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arXiv · 2107.11698

On quantitative uniqueness for parabolic equations

Igor Kukavica·Quinn Le
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Abstract

We consider the quantitative uniqueness properties for a parabolic type equation $ u_t-\Delta u = w(x,t) \nabla u + v(x,t) u$, when $v \in L^{p_2}_{t} L^{p_1}_x$ and $w \in L^{q_2}_{t} L^{q_1}_x$, with a suitable range for exponents $p_1$, $p_2$, $q_1$, and $q_2$. We prove a strong unique continuation property and provide a pointwise in time observability estimate.

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Igor Kukavica, Quinn Le. 2021-07-24. On quantitative uniqueness for parabolic equations. https://arxiv.org/abs/2107.11698

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