Smooth local solutions to weingarten equations and $\sigma_k$-equations

Tiancong Chen; Qing Han

Smooth local solutions to weingarten equations and $\sigma_k$-equations

Analysis of PDEs 2015-03-23 v1

Authors: Tiancong Chen , Qing Han

Abstract

In this paper, we study the existence of smooth local solutions to Weingarten equations and $\sigma_k$ -equations. We will prove that, for $2 \leq k \leq n$ , the Weingarten equations and the $\sigma_k$ -equations always have smooth local solutions regardless of the sign of the functions in the right-hand side of the equations. We will demonstrate that the associate linearized equations are uniformly elliptic if we choose the initial approximate solutions appropriately.

Cite

@article{arxiv.1503.05950,
  title  = {Smooth local solutions to weingarten equations and $\sigma_k$-equations},
  author = {Tiancong Chen and Qing Han},
  journal= {arXiv preprint arXiv:1503.05950},
  year   = {2015}
}

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