Mathematics

Prof. Giacomoni, Jacques
University of Pau, France

The main result of this work is a new extension of
the well-known inequality by D\\'{\\i}az and Saa which, in our case,
involves an anisotropic operator, such as the $p(x)$\\--Laplacian,
$\\Delta_{p(x)} u\\equiv \\mathrm{div} (|\\nabla u|^{p(x) - 2} \\nabla u)$.
Our present extension of this inequality enables us to establish
some new results on the uniqueness of solutions and comparison principles
for some anisotropic quasilinear elliptic and parabolic equations