scholarly journals Carleman estimates and unique continuation property for elliptic operators in Banach spaces

2013 ◽  
pp. 873-885
Author(s):  
Veli B. Shakhmurov
Keyword(s):  
Banach Spaces ◽  
Unique Continuation ◽  
Elliptic Operators ◽  
Carleman Estimates ◽  
Unique Continuation Property ◽  
Continuation Property

Carleman Estimates and Unique Continuation Property for Abstract Elliptic Equations

2011 ◽  
Author(s):  
Veli B. Shakhmurov ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
Zacharias Anastassi
Keyword(s):  
Elliptic Equations ◽  
Unique Continuation ◽  
Carleman Estimates ◽  
Unique Continuation Property ◽  
Continuation Property

scholarly journals Discrete Carleman estimates and three balls inequalities

2021 ◽  
Vol 60 (6) ◽  
Author(s):  
Aingeru Fernández-Bertolin ◽  
Luz Roncal ◽  
Angkana Rüland ◽  
Diana Stan
Keyword(s):  
Unique Continuation ◽  
Carleman Estimate ◽  
Carleman Estimates ◽  
Auxiliary Result ◽  
Logarithmic Convexity ◽  
Unique Continuation Property ◽  
Discrete Operators ◽  
Continuation Property ◽  
Discrete Setting ◽  
The Continuum

AbstractWe prove logarithmic convexity estimates and three balls inequalities for discrete magnetic Schrödinger operators. These quantitatively connect the discrete setting in which the unique continuation property fails and the continuum setting in which the unique continuation property is known to hold under suitable regularity assumptions. As a key auxiliary result which might be of independent interest we present a Carleman estimate for these discrete operators.

scholarly journals Strict monotonicity and unique continuation of the biharmonic operator - doi: 10.5269/bspm.v30i2.14502

1970 ◽  
Vol 30 (2) ◽  
pp. 79-83
Author(s):  
Najib Tsouli ◽  
Omar Chakrone ◽  
Mostafa Rahmani ◽  
Omar Darhouche
Keyword(s):  
Unique Continuation ◽  
Biharmonic Operator ◽  
Strict Monotonicity ◽  
Unique Continuation Property ◽  
Continuation Property

In this paper, we will show that the strict monotonicity of the eigenvalues of the biharmonic operator holds if and only if some unique continuation property is satisfied by the corresponding eigenfunctions.

scholarly journals Unique continuation for non-negative solutions of quasilinear elliptic equations

2001 ◽  
Vol 64 (1) ◽  
pp. 149-156 ◽  
Author(s):  
Pietro Zamboni
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Unique Continuation ◽  
Quasilinear Elliptic Equations ◽  
Kato Class ◽  
Unique Continuation Property ◽  
Continuation Property ◽  
Quasilinear Elliptic

Dedicated to Filippo ChiarenzaThe aim of this note is to prove the unique continuation property for non-negative solutions of the quasilinear elliptic equation We allow the coefficients to belong to a generalized Kato class.

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