JournalsrmiVol. 27, No. 2pp. 475–491

Quantitative uniqueness for second order elliptic operators with strongly singular coefficients

  • Ching-Lung Lin

    National Cheng Kung University, Tainan, Taiwan
  • Gen Nakamura

    Hokkaido University, Sapporo, Japan
  • Jenn-Nan Wang

    National Taiwan University, Taipei, Taiwan
Quantitative uniqueness for second order elliptic operators with strongly singular coefficients cover
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Abstract

In this paper we study the local behavior of a solution to second order elliptic operators with sharp singular coefficients in lower order terms. One of the main results is the bound on the vanishing order of the solution, which is a quantitative estimate of the strong unique continuation property. Our proof relies on Carleman estimates with carefully chosen phases. A key strategy in the proof is to derive doubling inequalities via three-sphere inequalities. Our method can also be applied to certain elliptic systems with similar singular coefficients.

Cite this article

Ching-Lung Lin, Gen Nakamura, Jenn-Nan Wang, Quantitative uniqueness for second order elliptic operators with strongly singular coefficients. Rev. Mat. Iberoam. 27 (2011), no. 2, pp. 475–491

DOI 10.4171/RMI/644