Unique continuation for the heat operator with potentials in weak spaces
Year: 2024
Type: article
Abstract: We prove strong unique continuation property for the differential inequality $|(\partial_t +Δ)u(x,t)|\le V(x,t)|u(x,t)|$ with $V$ contained in weak spaces. In particular, we establish the strong unique continuation property for $V\in L^\infty_t L^{d/2,\infty}_x$, 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.
Source: Analysis & PDE
Authors: Eunhee Jeong, Sanghyuk Lee, Jaehyeon Ryu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4401815094