On quantitative uniqueness for parabolic equations

2021/07/24 by Kukavica, Igor, Le, Quinn
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.11698

Abstract

We consider the quantitative uniqueness properties for a parabolic type equation ut-Δu = w(x,t) ∇ u + v(x,t) u, when v ∈ Lp2t Lp1x and w ∈ Lq2t Lq1x, with a suitable range for exponents p1, p2, q1, and q2. We prove a strong unique continuation property and provide a pointwise in time observability estimate.

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