On quantitative uniqueness for parabolic equations

Igor Kukavica; Quinn Le

paper

On quantitative uniqueness for parabolic equations

arXiv:2107.11698

Abstract

We consider the quantitative uniqueness properties for a parabolic type equation $u_{t} - Δ u = w (x, t) \nabla u + v (x, t) u$ , when $v \in L_{t}^{p_{2}} L_{x}^{p_{1}}$ and $w \in L_{t}^{q_{2}} L_{x}^{q_{1}}$ , 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.