A weak comparison principle for some quasilinear elliptic operators: it compares functions belonging to different spaces

摘要

We shall prove a weak comparison principle for quasilinear elliptic operators $-{m div}(a(x,abla u))$ that includes the negative $p$-Laplace operator, where $a: OmegaimesBbb R^N ightarrowBbb R^N$ satisfies certain conditions frequently seen in the research of quasilinear elliptic operators. In our result, it is characteristic that functions which are compared belong to different spaces.