Unique continuation for the heat operator with potentials in weak spaces

2021/09/22 by Eun-Hee Jeong, Jeong, Eunhee, Sang‐Hyuk Lee +3
Mathematics · #35B60 #35K05(primary) #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2109.10564

openalex publication_date 2021/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove strong unique continuation property for the differential inequality |(∂_t +Δ)u(x,t)|≤ V(x,t)|u(x,t)| with V contained in weak spaces. In particular, we establish the strong unique continuation property for V∈ L^∞_t L^d/2,∞_x, which has been left open since the works of Escauriaza [6] and Escauriaza-Vega [8]. Our results are consequences of the Carleman estimates for the heat operator in the Lorentz spaces.

Citations

• On the boundary convergence of solutions to the Hermite-Schrödinger equation

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