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).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a31/}
}
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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/