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

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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… Click to show full 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.

Keywords: different spaces; principle quasilinear; weak comparison; comparison principle; quasilinear elliptic; elliptic operators

Journal Title: Applications of Mathematics
Year Published: 2018

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