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• W2951694813 abstract "We consider the nonlinear problem [(P) ;; I u=f(x,u) text{ in $Omega$,} ;; u=0 text{ on $mathbb{R}^{N}setminusOmega$ }] in an open bounded set $Omegasubsetmathbb{R}^{N}$, where $I$ is a nonlocal operator which may be anisotropic and may have varying order. We assume mild symmetry and monotonicity assumptions on $I$, $Omega$ and the nonlinearity $f$ with respect to a fixed direction, say $x_1$, and we show that any nonnegative weak solution $u$ of $(P)$ is symmetric in $x_1$. Moreover, we have the following alternative: Either $uequiv 0$ in $Omega$, or $u$ is strictly decreasing in $|x_1|$. The proof relies on new maximum principles for antisymmetric supersolutions of an associated class of linear problems." @default.
• W2951694813 created "2019-06-27" @default.
• W2951694813 creator A5045719093 @default.
• W2951694813 creator A5062208839 @default.
• W2951694813 date "2014-06-24" @default.
• W2951694813 modified "2023-09-23" @default.
• W2951694813 title "Symmetry via antisymmetric maximum principles in nonlocal problems of variable order" @default.
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• W2951694813 hasPublicationYear "2014" @default.
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