Carleman inequalities and unique continuation for the polyharmonic operators

被引：0
作者：
Jeong, Eunhee [1 ,2 ]
Kwon, Yehyun [3 ]
Lee, Sanghyuk [4 ,5 ]
机构：
[1] Jeonbuk Natl Univ, Dept Math Educ, Jeonju 54896, South Korea
[2] Jeonbuk Natl Univ, Inst Pure & Appl Math, Jeonju 54896, South Korea
[3] Changwon Natl Univ, Dept Math, Chang Won 51140, South Korea
[4] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea
[5] Seoul Natl Univ, RIM, Seoul 151747, South Korea
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 385卷
关键词：
Carleman inequality; Unique continuation; Polyharmonic operator; BOCHNER-RIESZ OPERATORS; NEGATIVE INDEX; POWERS; LAPLACIAN; ORDER;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We obtain a complete characterization of Lp - Lq Carleman estimates with weight ev<middle dot>x for the polyharmonic operators. Our result extends the Carleman inequalities for the Laplacian due to Kenig-Ruiz-Sogge. Consequently, we obtain new unique continuation properties of higher order Schr & ouml;dinger equations relaxing the integrability assumption on the solution spaces. (c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页码：86 / 120
页数：35
相关论文
共 50 条
[41]   Unique continuation inequalities for Schrödinger equation on Riemannian symmetric spaces of noncompact type [J].
Mithun Bhowmik ;
Swagato K. Ray .
Annali di Matematica Pura ed Applicata (1923 -), 2024, 203 :331-343
[42]   The Generalized Davies Problem for Polyharmonic Operators [J].
Avkhadiev, F. G. .
SIBERIAN MATHEMATICAL JOURNAL, 2017, 58 (06) :932-942
[43]   The Generalized Davies Problem for Polyharmonic Operators [J].
F. G. Avkhadiev .
Siberian Mathematical Journal, 2017, 58 :932-942
[44]   UNIVERSAL BOUNDS FOR EIGENVALUES OF THE POLYHARMONIC OPERATORS [J].
Jost, Juergen ;
Li-Jost, Xianqing ;
Wang, Qiaoling ;
Xia, Changyu .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (04) :1821-1854
[45]   Scale-Free Unique Continuation Estimates and Applications to Random Schrödinger Operators [J].
Constanza Rojas-Molina ;
Ivan Veselić .
Communications in Mathematical Physics, 2013, 320 :245-274
[46]   A remark on unique continuation [J].
Yifei Pan ;
Thomas Wolff .
The Journal of Geometric Analysis, 1998, 8 (4) :599-604
[47]   A NOTE ON TWO WEIGHTED DISCRETE CARLEMAN INEQUALITIES [J].
Lai, Baofeng ;
Wang, Runqiu ;
Liu, Hao .
JOURNAL OF MATHEMATICAL INEQUALITIES, 2021, 15 (04) :1601-1611
[48]   Carleman estimates and inverse problems for Dirac operators [J].
Mikko Salo ;
Leo Tzou .
Mathematische Annalen, 2009, 344 :161-184
[49]   Carleman estimates and inverse problems for Dirac operators [J].
Salo, Mikko ;
Tzou, Leo .
MATHEMATISCHE ANNALEN, 2009, 344 (01) :161-184
[50]   Quantitative unique continuation for operators with partially analytic coefficients. Application to approximate control for waves [J].
Laurent, Camille ;
Leautaud, Matthieu .
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2019, 21 (04) :957-1069
12345