Carleman estimate for second order elliptic equations with Lipschitz leading coefficients and jumps at an interface

被引：15

作者：

Di Cristo, M. ^{[1
]}

Francini, E. ^{[2
]}

Lin, C. -L. ^{[3
]}

Vessella, S. ^{[2
]}

Wang, J. -N. ^{[4
]}

机构：

[1] Politecn Milan, Milan, Italy

[2] Univ Firenze, Florence, Italy

[3] Natl Cheng Kung Univ, Tainan, Taiwan

[4] Natl Taiwan Univ, Taipei, Taiwan

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2017年 / 108卷 / 02期

关键词：

Carleman estimate; Elliptic operator; Nonsmooth coefficient; DIVERGENCE FORM; DIFFERENTIAL-EQUATIONS; OPERATORS; CONTINUATION; UNIQUENESS;

D O I：

10.1016/j.matpur.2016.10.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove a local Carleman estimate for second order elliptic equations with a general anisotropic Lipschitz coefficients having a jump at an interface. The argument we use is of microlocal nature. Yet, not relying on pseudodifferential calculus, our approach allows one to achieve almost optimal assumptions on the regularity of the coefficients and, consequently, of the interface. (C) 2016 Elsevier Masson SAS. All rights reserved.

引用

页码：163 / 206

页数：44

共 17 条

[1] ELLIPTIC-EQUATIONS IN DIVERGENCE FORM, GEOMETRIC CRITICAL-POINTS OF SOLUTIONS, AND STEKLOFF EIGENFUNCTIONS [J].