Remarks on comparison principles for -Laplacian with extension to -Laplacian

Abstract

Our purpose is to generalize some recent comparison principles for operators driven by [Formula: see text]-Laplacian to a wide class of quasilinear equations including [Formula: see text]-Laplacian. It turns out, in particular, that adding a [Formula: see text]-Laplacian to [Formula: see text]-Laplacian allows to weaken the assumptions needed on the Hamiltonian of lower order terms. The results are specialized in the case that the Hamiltonian has at most polynomial growth in the gradient with coefficients depending on [Formula: see text] and [Formula: see text].

Keywords

• Quasilinear elliptic operators
• maximum principles
• comparison principles