English

Local pointwise second derivative estimates for strong solutions to the $\sigma_k$-Yamabe equation on Euclidean domains

Analysis of PDEs 2021-08-05 v2 Differential Geometry

Abstract

We prove local pointwise second derivative estimates for positive W2,pW^{2,p} solutions to the σk\sigma_k-Yamabe equation on Euclidean domains, addressing both the positive and negative cases. Generalisations for augmented Hessian equations are also considered.

Keywords

Cite

@article{arxiv.2009.06362,
  title  = {Local pointwise second derivative estimates for strong solutions to the $\sigma_k$-Yamabe equation on Euclidean domains},
  author = {Jonah A. J. Duncan and Luc Nguyen},
  journal= {arXiv preprint arXiv:2009.06362},
  year   = {2021}
}

Comments

Updated references, some notation clarified