The \(N\)-Laplacian elliptic equation: Variational versus entropy solutions (Q1922955)

The paper deals with the homogeneous Dirichlet problem in a bounded \(N\)-dimensional domain for the nonlinear \(N\)-Laplacian when the second member is assumed to be merely integrable. The standard concept of a variational (or energy) solution is compared with the concept of an entropy solution. The conditions on the second member, under which the solutions are bounded, are also discussed.