Multivalued homogeneous Neumann problem involving diffuse measure data and variable exponent (Q2809929)

In this paper, the authors study the following nonlinear homogeneous Neumann boundary value problem: NEWLINE\[NEWLINE \begin{aligned} &\mu \in \nabla\cdot a(x,\nabla u) + \beta(u) \quad \text{in } \Omega,\\ &a(x,\nabla u)\cdot\eta = 0 \quad \text{on } \partial\Omega, \end{aligned} NEWLINE\]NEWLINE where \(\mu\) is a bounded diffuse Radon measure, \(\beta\) is maximal monotone and \(a\) is a Leray-Lions operator satisfying a growth condition with a variable exponent: \(|a(x,w)| \leq c(j(x) + |w|^{p(x)-1})\). Under suitable assumptions, they establish the existence and uniqueness of a weak solution. The proofs rely on the Yoshida approximated problem.