Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Interior Hessian estimates for Sigma-2 equations in dimension three

Guohuan Qiu

Abstract

We prove a priori interior C2 estimate for σ_2 = f in R3, which generalizes Warren-Yuan's result.

Interior Hessian estimates for Sigma-2 equations in dimension three

Abstract

We prove a priori interior C2 estimate for σ_2 = f in R3, which generalizes Warren-Yuan's result.

Paper Structure

This paper contains 6 sections, 7 theorems, 116 equations.

Table of Contents

  1. Introduction
  2. Preliminary Lemmas
  3. Mean value inequality.
  4. Proof of the theroem
  5. Appendix
  6. Proof of (\ref{['eq:V-1']})

Key Result

Theorem 1

Let $u$ be a smooth solution to (eq:sigma2) on $B_{10}\subset\mathbb{R}^{3}$ with $\Delta u>0$. Then we have where $C$ depends only on $\|f\|_{C^{2}}$, $\|\frac{1}{f}\|_{L^{\infty}}$ and $||u||_{C^{1}}$.

Theorems & Definitions (18)

  • Theorem 1
  • Lemma 1
  • proof
  • Lemma 2
  • Lemma 3
  • proof
  • Claim 1
  • proof
  • Claim 2
  • proof
  • ...and 8 more