scholarly journals Existence and regularity results for semi‐linearized compressible 2D fluids with generalized diffusion

2021 ◽  
Author(s):  
Luca Bisconti
Keyword(s):  
Existence And Regularity Results ◽  
Regularity Results

Existence and regularity results for unilateral problems with degenerate coercivity

2019 ◽  
Vol 69 (6) ◽  
pp. 1351-1366 ◽  
Author(s):  
Hocine Ayadi ◽  
Rezak Souilah
Keyword(s):  
Penalty Method ◽  
Degenerate Coercivity ◽  
Unilateral Problems ◽  
Existence And Regularity Results ◽  
Regularity Results

Abstract In this paper we prove some existence and regularity results for nonlinear unilateral problems with degenerate coercivity via the penalty method.

Cylindrical optimal rearrangement problem leading to a new type obstacle problem

2018 ◽  
Vol 24 (2) ◽  
pp. 859-872 ◽  
Author(s):  
Hayk Mikayelyan
Keyword(s):  
Comparison Principle ◽  
Obstacle Problem ◽  
Normal Derivative ◽  
Force Function ◽  
Cylindrical Domain ◽  
New Type ◽  
Existence And Regularity Results ◽  
Regularity Results ◽  
Cylindrical Axis

An optimal rearrangement problem in a cylindrical domainΩ=D× (0, 1) is considered, under the constraint that the force function does not depend on thexnvariable of the cylindrical axis. This leads to a new type of obstacle problem in the cylindrical domain     Δu(x′,xn) =χ{v>0}(x′) +χ{v=0}(x′) [∂νu(x′,0) +∂νu(x′, 1)]arising from minimization of the functional     ∫Ω½;|∇u(x)|2+χ{v>0}(x′)u(x) dx,wherev(x′) =∫01u(x′,t)dt, and∂νuis the exterior normal derivative ofuat the boundary. Several existence and regularity results are proven and it is shown that the comparison principle does not hold for minimizers.

scholarly journals Existence of Solutions for Unbounded Elliptic Equations with Critical Natural Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Aziz Bouhlal ◽  
Abderrahmane El Hachimi ◽  
Jaouad Igbida ◽  
El Mostafa Sadek ◽  
Hamad Talibi Alaoui
Keyword(s):  
Elliptic Problem ◽  
Lebesgue Space ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Regularity Of Solutions ◽  
Natural Growth ◽  
Existence And Regularity Results ◽  
Regularity Results

We investigate existence and regularity of solutions to unbounded elliptic problem whose simplest model is {-div[(1+uq)∇u]+u=γ∇u2/1+u1-q+f  in  Ω,  u=0  on  ∂Ω,}, where 0<q<1, γ>0 and f belongs to some appropriate Lebesgue space. We give assumptions on f with respect to q and γ to show the existence and regularity results for the solutions of previous equation.

scholarly journals Existence and regularity results for fully nonlinear equations with singularities

2011 ◽  
Vol 354 (1) ◽  
pp. 377-400 ◽  
Author(s):  
Patricio Felmer ◽  
Alexander Quaas ◽  
Boyan Sirakov
Keyword(s):  
Nonlinear Equations ◽  
Fully Nonlinear Equations ◽  
Fully Nonlinear ◽  
Existence And Regularity Results ◽  
Regularity Results

Théorèmes d'existence en calcul des variations et applications à l'élasticité non linéaire

1988 ◽  
Vol 109 (1-2) ◽  
pp. 51-78 ◽  
Author(s):  
R. Tahraoui
Keyword(s):  
Nonlinear Elasticity ◽  
Existence And Regularity Results ◽  
Image Position ◽  
Regularity Results

SynopsisIn this paper, we study problems of the form:We obtain some existence and regularity results when Ω is either a ball or an annulus, without convexity hypothesis on g. We then apply these results to some shear problems in nonlinear elasticity.

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