Geodesic
Quasilinear elliptic problems with nonstandard growth
Electronic journal of differential equations, Tome 2011 (2011)
We prove the existence of solutions to Dirichlet problems associated with the $p(x)$-quasilinear elliptic equation Au = - div $a(x, u, u) = f$ (x, u, u). These solutions are obtained in Sobolev spaces with variable exponents.
Classification : 35J20, 35J25
Keywords: quasilinear elliptic equation, Sobolev spaces with variable exponent, image processing, Dirichlet problem 
@article{EJDE_2011__2011__a43,
     author = {Benboubker,  Mohamed Badr and Azroul,  Elhoussine and Barbara,  Abdelkrim},
     title = {Quasilinear elliptic problems with nonstandard growth},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1221.35165},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a43/}
}
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AU  - Azroul,  Elhoussine
AU  - Barbara,  Abdelkrim
TI  - Quasilinear elliptic problems with nonstandard growth
JO  - Electronic journal of differential equations
PY  - 2011
VL  - 2011
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%A Azroul,  Elhoussine
%A Barbara,  Abdelkrim
%T Quasilinear elliptic problems with nonstandard growth
%J Electronic journal of differential equations
%D 2011
%V 2011
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%G en
%F EJDE_2011__2011__a43
Benboubker,  Mohamed Badr; Azroul,  Elhoussine; Barbara,  Abdelkrim. Quasilinear elliptic problems with nonstandard growth. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a43/