JournalsjemsVol. 16, No. 11pp. 2433–2475

Observability inequalities and measurable sets

  • Jone Apraiz

    Universidad del Pais Vasco, Donostia-San Sebastian, Spain
  • Luis Escauriaza

    Universidad del Pais Vasco, Bilbao, Spain
  • Gengsheng Wang

    Wuhan University, Wuhan, Hubei, China
  • C. Zhang

    Wuhan University, Wuhan, Hubei, China
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Abstract

This paper presents two observability inequalities for the heat equation over Ω×(0,T)\Omega\times (0,T). In the first one, the observation is from a subset of positive measure in Ω×(0,T)\Omega\times (0,T), while in the second, the observation is from a subset of positive surface measure on Ω×(0,T)\partial\Omega\times (0,T). It also proves the Lebeau-Robbiano spectral inequality when Ω\Omega is a bounded Lipschitz and locally star-shaped domain. Some applications for the above-mentioned observability inequalities are provided.

Cite this article

Jone Apraiz, Luis Escauriaza, Gengsheng Wang, C. Zhang, Observability inequalities and measurable sets. J. Eur. Math. Soc. 16 (2014), no. 11, pp. 2433–2475

DOI 10.4171/JEMS/490