scholarly journals Nonlinear Kato Class and Unique Continuation of Eigenfunctions forp-Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
René Erlín Castillo ◽  
Julio C. Ramos Fernández
Keyword(s):  
Weight Function ◽  
Bounded Domain ◽  
Unique Continuation ◽  
Laplacian Operator ◽  
Kato Class ◽  
Basic Properties ◽  
Unique Continuation Property ◽  
Continuation Property

We study some basic properties of nonlinear Kato classMp(ℝn)andM~p(ℝn),respectively, for1<p<n.Also, we study the problem-div(|∇u|p-2∇u)+V|u|p-2u=0inΩ,whereΩis a bounded domain inℝnand the weight functionVis assumed to be not equivalent to zero and lies inM~p(Ω), in the case wherep<n. Finally, we establish the strong unique continuation property of the eigenfunction for thep-Laplacian operator in the case whereV∈M~p(Ω).

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.

scholarly journals Strong unique continuation of eigenfunctions forp-Laplacian operator

2001 ◽  
Vol 25 (3) ◽  
pp. 213-216 ◽  
Author(s):  
Islam Eddine Hadi ◽  
N. Tsouli
Keyword(s):  
Unique Continuation ◽  
Laplacian Operator ◽  
Unique Continuation Property ◽  
Continuation Property

We show the strong unique continuation property of the eigenfunctions forp-Laplacian operator in the casep<N.

scholarly journals Strong Unique Continuation for Solutions of ap(x)-Laplacian Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Johnny Cuadro ◽  
Gabriel López
Keyword(s):  
Elliptic Equation ◽  
Bounded Domain ◽  
Quasilinear Elliptic Equation ◽  
Unique Continuation ◽  
Smooth Bounded Domain ◽  
Unique Continuation Property ◽  
Continuation Property ◽  
Quasilinear Elliptic

We study the strong unique continuation property for solutions to the quasilinear elliptic equation-div(|∇u|p(x)-2∇u)+V(x)|u|p(x)-2u=0  in  ΩwhereV(x)∈LN/p(x)(Ω),Ωis a smooth bounded domain inℝN, and1<p(x)<NforxinΩ.

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.

Local state observation for stochastic hyperbolic equations

2020 ◽  
Vol 26 ◽  
pp. 79
Author(s):  
Qi Lü ◽  
Zhongqi Yin
Keyword(s):  
Boundary Conditions ◽  
Hyperbolic Equations ◽  
Unique Continuation ◽  
Local State ◽  
Carleman Estimate ◽  
State Observation ◽  
Unique Continuation Property ◽  
Continuation Property ◽  
Global Carleman Estimate

In this paper, we solve a local state observation problem for stochastic hyperbolic equations without boundary conditions, which is reduced to a local unique continuation property for these equations. This result is proved by a global Carleman estimate. As far as we know, this is the first result in this topic.

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