Geodesic
Existence and uniqueness of weak and entropy solutions for homogeneous Neumann boundary-value problems involving variable exponents
Electronic journal of differential equations, Tome 2012 (2012)
In this article we study the nonlinear homogeneous Neumann boundary-value problem

$\displaylines{ b(u)-\hbox{div} a(x,\nabla u)=f\quad \hbox{in } \Omega\cr a(x,\nabla u).\eta=0 \quad\hbox{on }\partial \Omega, }$

where $\Omega$ is a smooth bounded open domain in $\mathbb{R}^{N}, N \geq 3$ and $\eta$ the outer unit normal vector on $\partial\Omega$. We prove the existence and uniqueness of a weak solution for $f \in L^{\infty}(\Omega)$ and the existence and uniqueness of an entropy solution for $L^{1}$-data $f$. The functional setting involves Lebesgue and Sobolev spaces with variable exponents.
Classification : 35J20, 35J25, 35D30, 35B38, 35J60
Keywords: elliptic equation, weak solution, entropy solution, Leray-lions operator, variable exponent 
@article{EJDE_2012__2012__a31,
     author = {Bonzi,  Bernard K. and Nyanquini,  Ismael and Ouaro,  Stanislas},
     title = {Existence and uniqueness of weak and entropy solutions for homogeneous {Neumann} boundary-value problems involving variable exponents},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1239.35044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a31/}
}
TY  - JOUR
AU  - Bonzi,  Bernard K.
AU  - Nyanquini,  Ismael
AU  - Ouaro,  Stanislas
TI  - Existence and uniqueness of weak and entropy solutions for homogeneous Neumann boundary-value problems involving variable exponents
JO  - Electronic journal of differential equations
PY  - 2012
VL  - 2012
UR  - http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a31/
LA  - en
ID  - EJDE_2012__2012__a31
ER  - 
%0 Journal Article
%A Bonzi,  Bernard K.
%A Nyanquini,  Ismael
%A Ouaro,  Stanislas
%T Existence and uniqueness of weak and entropy solutions for homogeneous Neumann boundary-value problems involving variable exponents
%J Electronic journal of differential equations
%D 2012
%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a31/
%G en
%F EJDE_2012__2012__a31
Bonzi,  Bernard K.; Nyanquini,  Ismael; Ouaro,  Stanislas. Existence and uniqueness of weak and entropy solutions for homogeneous Neumann boundary-value problems involving variable exponents. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a31/