Regularity results for the equation $u_{11}u_{22} = 1$

Connor Mooney; Ovidiu Savin

Regularity results for the equation $u_{11}u_{22} = 1$

Analysis of PDEs 2018-06-15 v1

Authors: Connor Mooney , Ovidiu Savin

Abstract

We study the equation $u_{11}u_{22} = 1$ in $\mathbb{R}^2$ . Our results include an interior $C^2$ estimate, classical solvability of the Dirichlet problem, and the existence of non-quadratic entire solutions. We also construct global singular solutions to the analogous equation in higher dimensions. At the end we state some open questions.

Keywords

dirichlet problem regularity for elliptic equations regularity theory

Cite

@article{arxiv.1806.05532,
  title  = {Regularity results for the equation $u_{11}u_{22} = 1$},
  author = {Connor Mooney and Ovidiu Savin},
  journal= {arXiv preprint arXiv:1806.05532},
  year   = {2018}
}

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