The capacity for pseudomonotone operators (Q1841544)

The notion of capacity relative to the \(p\)-Laplacian is well known; recently \textit{G. Dal Maso} and \textit{I. V. Skrypnik} [Potential Anal. 7, No. 4, 765-803 (1997; Zbl 0887.31005)] have given a notion of capacity relative to nonlinear elliptic monotone operators of the type \(-\text{div}(a(x,\nabla u))\) and have used this notion to study the homogenization of a homogeneous Dirichlet problem with holes for the above operator. The author generalizes the notion of capacity to elliptic monotone operators of the type \(-\text{div}(a(x, u,\nabla u))\) and uses it to study the homogenization of a homogeneous Dirichlet problem with holes for the considered operator.