Liouville theorems for stable radial solutions for the biharmonic operator

2010 ◽  
Vol 69 (1-2) ◽  
pp. 87-98 ◽  
Author(s):  
Guillaume Warnault
Keyword(s):  
Biharmonic Operator ◽  
Radial Solutions ◽  
Liouville Theorems

Radial solutions of inhomogeneous fourth order elliptic equations and weighted Sobolev embeddings

2015 ◽  
Vol 4 (2) ◽  
pp. 135-151 ◽  
Author(s):  
Reginaldo Demarque ◽  
Olimpio H. Miyagaki
Keyword(s):  
Fourth Order ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Continuous Functions ◽  
Existence Results ◽  
Compact Embedding ◽  
Biharmonic Operator ◽  
Radial Solutions ◽  
Sobolev Embeddings ◽  
Fourth Order Elliptic Equations

AbstractWe deal with a class of inhomogeneous elliptic problems involving the biharmonic operator Δ2u + V(|x|)|u|q-2u = Q(|x|)f(u), u ∈ D02,2(ℝN), where Δ2 is the biharmonic operator and V, Q are singular continuous functions. Compact embedding results are established and by using these facts some existence results are obtained.

scholarly journals The exterior Dirichlet problems of Monge–Ampère equations in dimension two

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Limei Dai
Keyword(s):  
Asymptotic Behavior ◽  
Unit Ball ◽  
Bounded Domain ◽  
Viscosity Solutions ◽  
Sufficient Conditions ◽  
Radial Solutions ◽  
Dirichlet Problems ◽  
Necessary And Sufficient ◽  
Monge Ampere ◽  
Prescribed Asymptotic Behavior

AbstractIn this paper, we study the Monge–Ampère equations $\det D^{2}u=f$ det D 2 u = f in dimension two with f being a perturbation of $f_{0}$ f 0 at infinity. First, we obtain the necessary and sufficient conditions for the existence of radial solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a unit ball. Then, using the Perron method, we get the existence of viscosity solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a bounded domain.

scholarly journals On the decay of the energy for radial solutions in Moore–Gibson–Thompson thermoelasticity

2021 ◽  
pp. 108128652199425
Author(s):  
Noelia Bazarra ◽  
José R Fernández ◽  
Ramón Quintanilla
Keyword(s):  
Numerical Simulations ◽  
Exponential Decay ◽  
Time Variable ◽  
Radial Solutions ◽  
Radially Symmetric Solutions ◽  
Thermoelastic Theory

In this paper, we consider the Moore–Gibson–Thompson thermoelastic theory. We restrict our attention to radially symmetric solutions and we prove the exponential decay with respect to the time variable. We demonstrate this fact with the help of energy arguments. Later, we give some numerical simulations to illustrate this behaviour.

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.

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