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 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 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 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 Eigenvalue problems for a quasilinear elliptic equation onℝN

2005 ◽  
Vol 2005 (18) ◽  
pp. 2871-2882 ◽  
Author(s):  
Marilena N. Poulou ◽  
Nikolaos M. Stavrakakis
Keyword(s):  
Elliptic Equation ◽  
Weight Function ◽  
Quasilinear Elliptic Equation ◽  
Eigenvalue Problems ◽  
Principal Eigenvalue ◽  
Laplacian Operator ◽  
Quasilinear Elliptic

We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation−Δpu=λg(x)|u|p−2u,x∈ℝN,lim|x|→+∞u(x)=0, whereΔpu=div(|∇u|p−2∇u)is thep-Laplacian operator and the weight functiong(x), being bounded, changes sign and is negative and away from zero at infinity.

Existence of Radial Solutions for Quasilinear Elliptic Equations with Singular Nonlinearities

2003 ◽  
Vol 3 (4) ◽  
Author(s):  
Beatrice Acciaio ◽  
Patrizia Pucci
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Quasilinear Elliptic Equations ◽  
Radial Solutions ◽  
Singular Nonlinearities ◽  
Quasilinear Elliptic

AbstractWe prove the existence of radial solutions of the quasilinear elliptic equation div(A(|Du|)Du) + f(u) = 0 in ℝ

scholarly journals Norm Comparison Estimates for the Composite Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xuexin Li ◽  
Yong Wang ◽  
Yuming Xing
Keyword(s):  
Elliptic Equation ◽  
Quasilinear Elliptic Equation ◽  
Differential Forms ◽  
Generalized Solution ◽  
Composite Operator ◽  
Potential Operator ◽  
Norm Estimates ◽  
Quasilinear Elliptic ◽  
Littlewood Maximal Operator ◽  
Norm Comparison

This paper obtains the Lipschitz and BMO norm estimates for the composite operator𝕄s∘Papplied to differential forms. Here,𝕄sis the Hardy-Littlewood maximal operator, andPis the potential operator. As applications, we obtain the norm estimates for the Jacobian subdeterminant and the generalized solution of the quasilinear elliptic equation.

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