Comparison principles for the \(p\)-Laplacian operator (Q2258283)

In this paper the author proves new comparison principles for the \(p\)-Laplace operator, both in bounded and in unbounded domains. In bounded domains he applies an approach already developed in the literature for the case where \(1 < p\leq 2\), and extends it to the case \(p > 2\), using measure theory. In unbounded domains the author combines this approach with the nonlinear capacity method based on algebraic operations and the choice of suitable test functions in the weak formulation of the problem under consideration. The last section of the paper is devoted to an application of the comparison principle to the proof of the Liouville type theorem for a quasilinear Dirichlet problem in the half-space.