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- W4288282005 abstract "We consider the elliptic equation $-Delta u = u^q|nabla u|^p$ in $mathbb R^n$ for any $pge 2$ and $q>0$. We prove a Liouville-type theorem, which asserts that any positive bounded solution is constant. The proof technique is based on monotonicity properties for the spherical averages of sub- and super-harmonic functions, combined with a gradient bound obtained by a local Bernstein argument. This solves, in the case of bounded solutions, a problem left open in~cite{BVGHV}, where the authors consider the case $0<p<2$. Some extensions to elliptic systems are also given." @default.
- W4288282005 created "2022-07-28" @default.
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- W4288282005 date "2019-07-15" @default.
- W4288282005 modified "2023-09-28" @default.
- W4288282005 title "A Liouville-type theorem for an elliptic equation with superquadratic growth in the gradient" @default.
- W4288282005 doi "https://doi.org/10.48550/arxiv.1907.06816" @default.
- W4288282005 hasPublicationYear "2019" @default.
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