scholarly journals ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

2014 ◽  
Vol 34 (3) ◽  
pp. 931-957 ◽  
Author(s):  
Luca Calatroni ◽  
◽  
Bertram Düring ◽  
Carola-Bibiane Schönlieb ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Image Processing ◽  
Partial Differential Equation ◽  
Fourth Order ◽  
Nonlinear Partial Differential Equation ◽  
Splitting Schemes ◽  
Partial Differential

scholarly journals On a Class of PDE Involving p-Biharmonic Operator

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Abdelouahed El Khalil
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fourth Order ◽  
Mountain Pass Theorem ◽  
Nonlinear Partial Differential Equation ◽  
Existence Of Solution ◽  
Mountain Pass ◽  
Biharmonic Operator ◽  
Partial Differential

The existence of solution for a fourth-order nonlinear partial differential equation (PDE) class involving p-biharmonic operator Δ(|Δu|p−2Δu)=λρ(x)|u|q−2u  in  Ω,  u=Δu=0,  on⁡  ∂Ω, is proved by applying mountain pass theorem and a local minimization.

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