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A Weak Comparison Principle for Some Quasilinear Elliptic Operators: It Compares Functions Belonging to Different Spaces

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Abstract

We shall prove a weak comparison principle for quasilinear elliptic operators −div(a(x,∇u)) that includes the negative p-Laplace operator, where a: × ℝN → ℝN 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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  1. Department of Applied Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, 162-0825, Japan

    Akihito Unai

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  1. Akihito Unai
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Correspondence to Akihito Unai.

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Unai, A. A Weak Comparison Principle for Some Quasilinear Elliptic Operators: It Compares Functions Belonging to Different Spaces. Appl Math 63, 483–498 (2018). https://doi.org/10.21136/AM.2018.0126-18

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  • DOI: https://doi.org/10.21136/AM.2018.0126-18

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