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Keywords:
weak comparison principle; quasilinear elliptic operator; $p$-Laplace operator
Summary:
We shall prove a weak comparison principle for quasilinear elliptic operators $-{\rm div}(a(x,\nabla u))$ that includes the negative $p$-Laplace operator, where $a\colon \Omega \times \Bbb R^N \rightarrow \Bbb R^N$ 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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