Geodesic
A weak comparison principle for some quasilinear elliptic operators: it compares functions belonging to different spaces
Applications of Mathematics, Tome 63 (2018) no. 4, pp. 483-498.

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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.
DOI : 10.21136/AM.2018.0126-18
Classification : 35B51, 35J25, 35J62, 35J92
Keywords: weak comparison principle; quasilinear elliptic operator; $p$-Laplace operator 
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Unai, Akihito. A weak comparison principle for some quasilinear elliptic operators: it compares functions belonging to different spaces. Applications of Mathematics, Tome 63 (2018) no. 4, pp. 483-498. doi : 10.21136/AM.2018.0126-18. http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0126-18/

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