- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:46
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
27
2011
2
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
Carleman estimates, three-sphere inequalities, doubling inequalities
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.
Partial differential equations
General
475
491
10.4171/RMI/644
http://www.ems-ph.org/doi/10.4171/RMI/644