Weighted gradient inequalities and unique continuation problems

被引：0

作者：

De Carli, Laura ^{[1
]}

Gorbachev, Dmitry ^{[2
]}

Tikhonov, Sergey ^{[3
]}

机构：

[1] Florida Int Univ, Dept Math, Miami, FL 33199 USA

[2] Tula State Univ, Dept Appl Math & Comp Sci, Tula 300012, Russia

[3] UAB, Ctr Recerca Matemat, ICREA, Campus Bellaterra,Edifici C, Barcelona 08193, Spain

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2020年 / 59卷 / 03期

基金：

俄罗斯科学基金会;

关键词：

ELLIPTIC-SYSTEMS; NORM INEQUALITIES; SOBOLEV INEQUALITIES; POSITIVE EIGENVALUES; PROPERTY; CONSTANT; DIRAC; OPERATORS; THEOREMS; ABSENCE;

D O I：

10.1007/s00526-020-1716-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use Pitt inequalities for the Fourier transform to prove the following weighted gradient inequality parallel to e(-tau l(.)) u(1/q) f parallel to(q) <= c(tau)parallel to e(-tau l(.)) v(1/p) del f parallel to(p), f is an element of C-0(infinity) (R-n). This inequality is a Carleman-type estimate that yields unique continuation results for solutions of first order differential equations and systems.

引用

页数：24

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