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Optimal three-ball inequality, quantitative uniqueness for the bi-Laplace equations
  • Xiaoyu FU,
  • Zhonghua LIAO
Xiaoyu FU
Sichuan University
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Zhonghua LIAO
Sichuan University
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Abstract

In this paper, we prove an optimal three-ball inequality for bi-Laplace equation in some open, connected set. The derivation of such estimate relies on a delicate Carleman estimate for the bi-Laplace equation and some Caccioppoli inequalities to estimate the lower-ters. Based on three -ball inequality, we then derive the vanishing order of solutions, which is a quantitative version of the strong unique continuation property.

Peer review status:ACCEPTED

17 Nov 2020Submitted to Mathematical Methods in the Applied Sciences
18 Nov 2020Submission Checks Completed
18 Nov 2020Assigned to Editor
21 Nov 2020Reviewer(s) Assigned
16 Feb 2021Review(s) Completed, Editorial Evaluation Pending
24 Feb 2021Editorial Decision: Revise Minor
20 Mar 20211st Revision Received
20 Mar 2021Submission Checks Completed
20 Mar 2021Assigned to Editor
20 Mar 2021Editorial Decision: Accept