Solvability of the dirichlet problem for a class of degenerate quasilinear elliptic equations

1983 ◽  
Vol 22 (2) ◽  
pp. 1274-1280 ◽  
Author(s):  
P. Z. Mkrtychyan
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Quasilinear Elliptic

scholarly journals Existence of Renormalized Solutions for Some Anisotropic Quasilinear Elliptic Equations

2020 ◽  
Vol 44 (4) ◽  
pp. 617-637
Author(s):  
T. AHMEDATT ◽  
A. AHMED ◽  
H. HJIAJ ◽  
A. TOUZANI
Keyword(s):  
Dirichlet Problem ◽  
Growth Condition ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Renormalized Solutions ◽  
Carathéodory Function ◽  
Regularity Results ◽  
Quasilinear Elliptic

In this paper, we consider a class of anisotropic quasilinear elliptic equations of the type ( | ∑N { − ∂ia (x, u, ∇u ) + |u|s(x )− 1u = f (x,u ), in Ω, i |( i=1 u = 0 on ∂ Ω, where f(x,s) is a Carathéodory function which satisfies some growth condition. We prove the existence of renormalized solutions for our Dirichlet problem, and some regularity results are concluded.

Radial solutions of the Dirichlet problem for a class of quasilinear elliptic equations arising in optometry

2019 ◽  
Vol 181 ◽  
pp. 9-23 ◽  
Author(s):  
Chiara Corsato ◽  
Colette De Coster ◽  
Noemi Flora ◽  
Pierpaolo Omari
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Radial Solutions ◽  
Quasilinear Elliptic
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