Noufou Sawadogo, Stanislas Ouaro

Multivalued Nonlinear Dirichlet Boundary p(u)-Laplacian Problem

abstract:
We study the following nonlinear homogenous Dirichlet boundary $p(u)$-Laplacian problem
$$ \beta(u)-\divv a(x,u,\nabla u)\ni f \;\;\text{in $\Omega$}, \;\;u=0\;\;\text{on $\partial\Omega$}. $$
The existence and partial uniqueness results of solutions for $L^{1}$-data $f$ are established.

Mathematics Subject Classification: 35J25, 35J60, 35Dxx, 76A05

Key words and phrases: Variable exponent $p(u)$-Laplacian, Young measure, homogeneous Dirichlet boundary condition, bounded Radon diffuse measures, maximal monotone graph