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• W2077394054 abstract "We study relations between the k-Hessian energy , and the fractional Sobolev energy , where Fk (k = 1, . . . , n) is the k-Hessian operator on ℝn, and u is a k-convex function vanishing at ∞. We prove that there is a constant C > 0 such that C−1Ek[u] ≦ ℰk[u] ≦ CEk[u], where the lower estimate is obtained under some additional assumptions on u. In general, we show that there exists a function ũ such that c−1 ≦ |u/ũ| ≦ c, and C−1Ek[ũ] ≦ ℰk[u] ≦ CEk[ũ], where c, C are positive constants depending only on k and n." @default.
• W2077394054 created "2016-06-24" @default.
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• W2077394054 date "2012-01-01" @default.
• W2077394054 modified "2023-09-26" @default.
• W2077394054 title "Hessian inequalities and the fractional Laplacian" @default.
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• W2077394054 doi "https://doi.org/10.1515/crelle.2011.116" @default.
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