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• W2921559139 endingPage "106855" @default.
• W2921559139 startingPage "106855" @default.
• W2921559139 abstract "We prove that the principal eigenvalue of any fully nonlinear homogeneous elliptic operator which fulfills a very simple convexity assumption satisfies a Brunn-Minkowski type inequality on the class of open bounded sets in $mathbb{R}^n$ satisfying a uniform exterior sphere condition. In particular the result applies to the (possibly normalized) $p$-Laplacian, and to the minimal Pucci operator. The proof is inspired by the approach introduced by Colesanti for the principal frequency of the Laplacian within the class of convex domains, and relies on a generalization of the convex envelope method by Alvarez-Lasry-Lions. We also deal with the existence and log-concavity of positive viscosity eigenfunctions." @default.
• W2921559139 created "2019-03-22" @default.
• W2921559139 creator A5048895218 @default.
• W2921559139 creator A5054582414 @default.
• W2921559139 date "2020-01-01" @default.
• W2921559139 modified "2023-10-08" @default.
• W2921559139 title "The Brunn–Minkowski inequality for the principal eigenvalue of fully nonlinear homogeneous elliptic operators" @default.
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• W2921559139 doi "https://doi.org/10.1016/j.aim.2019.106855" @default.
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