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Convexity of solutions to boundary blow-up problems

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  • We prove convexity of solutions to boundary blow-up problems for the singular infinity Laplacian and the $p$-Laplacian for $p\ge 2$. The proof is based on an extension of the results of Alvarez, Lasry and Lions [2] and on estimates of the boundary blow-up rate.
    Mathematics Subject Classification: 35J60, 35J65, 26B25.


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