TheN-Laplacian Elliptic Equation: Variational versus Entropy Solutions

@article{Boccardo1996TheNLaplacianEE,
  title={TheN-Laplacian Elliptic Equation: Variational versus Entropy Solutions},
  author={Lucio Boccardo and I. Peral and Juan Luis V{\'a}zquez},
  journal={Journal of Mathematical Analysis and Applications},
  year={1996},
  volume={201},
  pages={671-688}
}
Abstract The N -Laplacian equation −∇·(|∇ u | N −2 ∇ u )= f is a kind of limit case in the existence theory of nonlinear elliptic equations when the second member is assumed to be merely integrable ( L 1 theory). Here we consider for definiteness the solutions of the homogeneous Dirichlet problem in a bounded domain Ω∈ R N and compare the standard concept of a variational (or energy) solution with the recently introduced concept of an entropy solution, which seems natural in the L 1 theory. For… 
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