Archive for Rational Mechanics and Analysis

, Volume 168, Issue 3, pp 245–252

Quasiconvex Functions and Hessian Equations

  • Daniel Faraco
  • Xiao Zhong

DOI: 10.1007/s00205-003-0255-8

Cite this article as:
Faraco, D. & Zhong, X. Arch. Rational Mech. Anal. (2003) 168: 245. doi:10.1007/s00205-003-0255-8


n×n of symmetric matrices. They are built on the k-th elementary symmetric function of the eigenvalues, k=1,2,…,n. Our motivation came from a paper by Šverák [S]. The proof of our result relies on the theory of the so-called k-Hessian equations, which have been intensively studied recently; see [CNS,T1,TW1,TW2].

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Daniel Faraco
    • 1
  • Xiao Zhong
    • 2
  1. 1.University of Jyväskylä, Department of Mathematics and Statistics and Max-Planck Institute, Leipzig, e-mail:
  2. 2.Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences and University of Jyväskylä, Department of Mathematics and Statistics, e-mail: