Quantitative Unique Continuation for Second Order Elliptic Operators with Singular Coefficients

被引：4

作者：

Tu Nguyen ^{[1
]}

机构：

[1] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet, Hanoi, Vietnam

来源：

VIETNAM JOURNAL OF MATHEMATICS | 2021年 / 49卷 / 04期

关键词：

Carleman estimate; Doubling inequality; Strong unique continuation;

D O I：

10.1007/s10013-020-00386-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish some quantitative strong unique continuation properties for solution of |Pu|<= C-1|x|(- 1)| backward difference u| + C-0|x|(- 2)|u| where P is a second order elliptic operator. As in (Rev. Mat. Iberoam. 27: 475-491, 9), our result is of quantitative nature but requires weaker conditions on the coefficients of P.

引用

页码：1001 / 1009

页数：9

共 50 条

[31] Strongly elliptic operators with singular coefficients
M. I. Neiman-zade
A. A. Shkalikov
Russian Journal of Mathematical Physics, 2006, 13 : 70 - 78
[32] Quantitative unique continuation for Schrodinger operators
Davey, Blair
JOURNAL OF FUNCTIONAL ANALYSIS, 2020, 279 (04)
[33] Unique continuation for operators with partially analytic coefficients
Tataru, D
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1999, 78 (05): : 505 - 521
[34] Unique Continuation of Solutions of Second-Order Quasi-Elliptic Equations
N. A. Shananin
Mathematical Notes, 2020, 108 : 302 - 306
[35] Unique Continuation of Solutions of Second-Order Quasi-Elliptic Equations
Shananin, N. A.
MATHEMATICAL NOTES, 2020, 108 (1-2) : 302 - 306
[36] Unique Continuation for the Elasticity System and a Counterexample for Second-Order Elliptic Systems
Kenig, Carlos
Wang, Jenn-Nan
HARMONIC ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, COMPLEX ANALYSIS, BANACH SPACES, AND OPERATOR THEORY, VOL 1: CELEBRATING CORA SADOSKY'S LIFE, 2016, 4 : 159 - 178
[37] POINCARE PROBLEM FOR A SECOND-ORDER ELLIPTIC EQUATION WITH SINGULAR COEFFICIENTS
DZHURAEV, A
DOKLADY AKADEMII NAUK SSSR, 1962, 146 (05): : 995 - &
[38] The weight problem for a second-order elliptic equation with singular coefficients
Devdariani, GG
DIFFERENTIAL EQUATIONS, 1996, 32 (03) : 352 - 355
[39] Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients
Koch, Herbert
Tataru, Daniel
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2009, 34 (04) : 305 - 366
[40] A quantitative Carleman estimate for second-order elliptic operators
Nakic, Ivica
Rose, Christian
Tautenhahn, Martin
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2019, 149 (04) : 915 - 938

← 1 2 3 4 5 →