Optimal function spaces for the weak continuity of the distributional k-Hessian

2018/04/03 by Tu, Qiang, Chen, Wenyi
#42B35 #46E35 #46F10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.00790

Abstract

In this paper we introduce the notion of distributional k-Hessian associated with Besov type functions in Euclidean n-space, k=2,…,n. Particularly, inspired by recent work of Baer and Jerison on distributional Hessian determinant, we show that the distributional k-Hessian is weak continuous on the Besov space B(2-(2)/(k),k), and the result is optimal in the framework of the space B(s,p), i.e., the distributional k-Hessian is well defined in B(s,p) if and only if B(s,p)⊂ B_loc(2-(2)/(k),k).

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