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Estimates for k -Hessian operator and some applications

Dongrui Wan (2013)

Czechoslovak Mathematical Journal

The k -convex functions are the viscosity subsolutions to the fully nonlinear elliptic equations F k [ u ] = 0 , where F k [ u ] is the elementary symmetric function of order k , 1 k n , of the eigenvalues of the Hessian matrix D 2 u . For example, F 1 [ u ] is the Laplacian Δ u and F n [ u ] is the real Monge-Ampère operator det D 2 u , while 1 -convex functions and n -convex functions are subharmonic and convex in the classical sense, respectively. In this paper, we establish an approximation theorem for negative k -convex functions, and give several...

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