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arXiv · 2109.10564

Unique continuation for the heat operator with potentials in weak spaces

Eunhee Jeong·Sanghyuk Lee·Jaehyeon Ryu
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Abstract

We prove strong unique continuation property for the differential inequality $|(\partial_t +\Delta)u(x,t)|\le V(x,t)|u(x,t)|$ 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.

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Eunhee Jeong, Sanghyuk Lee, Jaehyeon Ryu. 2021-09-22. Unique continuation for the heat operator with potentials in weak spaces. https://arxiv.org/abs/2109.10564

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