English

Very weak solutions of quadratic Hessian equations

Analysis of PDEs 2024-09-16 v1 Complex Variables

Abstract

We extend the methods of Lewicka - Pakzad, Sz\'ekelyhidi - Cao and Li - Qiu to study the notion of very weak solutions to the complex σ2\sigma_2 equation in domains in Cn, n2\mathbb C^n,\ n\geq 2. As a by-product we sharpen the regularity threshold of the counterexamples obtained by Li and Qiu in the real case.

Cite

@article{arxiv.2409.08852,
  title  = {Very weak solutions of quadratic Hessian equations},
  author = {Sławomir Dinew and Szymon Myga},
  journal= {arXiv preprint arXiv:2409.08852},
  year   = {2024}
}