Unique continuation for the heat operator with potentials in weak spaces

Eunhee Jeong; Sanghyuk Lee; Jaehyeon Ryu

Unique continuation for the heat operator with potentials in weak spaces

Analysis of PDEs 2022-05-31 v2

Authors: Eunhee Jeong , Sanghyuk Lee , Jaehyeon Ryu

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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@article{arxiv.2109.10564,
  title  = {Unique continuation for the heat operator with potentials in weak spaces},
  author = {Eunhee Jeong and Sanghyuk Lee and Jaehyeon Ryu},
  journal= {arXiv preprint arXiv:2109.10564},
  year   = {2022}
}

Comments

The current paper is the last section of the paper Hermite spectral projection operator (arXiv:2006.11762v2). The previous paper will remain unpublished

Unique continuation for the heat operator with potentials in weak spaces

Abstract

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