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• W1978761661 abstract "The k-convex functions are the viscosity subsolutions to the fully nonlinear elliptic equations Fk[u]=0, where Fk[u] is the elementary symmetric function of order k of the eigenvalues of Hessian matrix D2u, k=1,…,n. For example, F1[u] is the Laplacian Δu and Fn[u] is the real Monge–Ampère operator detD2u, while 1-convex functions and n-convex functions are subharmonic and convex in the classical sense, respectively. In this paper, we generalize the method of pluripotential theory for complex Monge–Ampère operator to that for the k-Hessian operator to establish the Lelong–Jensen type formula for real k-convex functions, show the comparison theorem for the k-Hessian boundary measure and introduce the generalized Lelong number for k-convex functions. We also show a relationship between the k-Hessian boundary measure and the generalized Lelong number. Les fonctions k-convexes sont les sousolutions de viscosité des équations elliptiques entièrement nonlinéaires Fk[u]=0, où Fk[u] est la fonction symétrique élémentaire á lʼordre k des valeurs propres de la matrice hessienne D2u, k=1,…,n. Par exemple, F1[u] est lʼopérateur Laplace Δu et Fn[u] est lʼopérateur de Monge–Ampère detD2u, alors que les fonctions 1-convexe et les fonctions n-convexes sont subharmoniques et convexes au sens classique, respectivement. Dans cet article, on généralise la méthode de la théorie pluripotentielle lʼopérateur de Monge–Ampère complexe celle pour que lʼopérateur de k-hessiens établisse le formule de type Lelong–Jensen pour fonctions k-convexes. Cela montre le théorème de comparaison pour la mesure k-hessiens de frontière et présente le nombre généralisé de Lelong pour des fonctions k-convexes. On montre également la relation entre la mesure k-hessiens de frontière et le nombre généralisé de Lelong." @default.
• W1978761661 created "2016-06-24" @default.
• W1978761661 creator A5037988079 @default.
• W1978761661 creator A5046597133 @default.
• W1978761661 date "2013-06-01" @default.
• W1978761661 modified "2023-09-28" @default.
• W1978761661 title "Lelong–Jensen type formula, k -Hessian boundary measure and Lelong number for k -convex functions" @default.
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• W1978761661 doi "https://doi.org/10.1016/j.matpur.2012.10.002" @default.
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