In this paper, we would like to derive a quantitative uniqueness estimate, the three-region inequality, for the second order elliptic equation with jump discontinuous coefficients. The derivation of the inequality relies on the Carleman estimate proved in our previous work. We then apply the three-region inequality to study the size estimate problem with one boundary measurement.
Three-region inequalities for the second order elliptic equation with discontinuous coefficients and size estimate / Francini, E.; Lin, C.-L.; Vessella, S.; Wang, J.-N.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 261:(2016), pp. 5306-5323. [10.1016/j.jde.2016.08.002]
Three-region inequalities for the second order elliptic equation with discontinuous coefficients and size estimate
FRANCINI, ELISA;VESSELLA, SERGIO;
2016
Abstract
In this paper, we would like to derive a quantitative uniqueness estimate, the three-region inequality, for the second order elliptic equation with jump discontinuous coefficients. The derivation of the inequality relies on the Carleman estimate proved in our previous work. We then apply the three-region inequality to study the size estimate problem with one boundary measurement.
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