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

Akihito Unai — 2018

Applications of Mathematics

We shall prove a weak comparison principle for quasilinear elliptic operators $- div (a (x, \nabla u))$ that includes the negative $p$ -Laplace operator, where $a : Ω \times ℝ^{N} \to ℝ^{N}$ 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.

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