二次黑森方程的极弱解

arXiv - MATH - Complex Variables Pub Date : 2024-09-13 DOI:arxiv-2409.08852

Sławomir Dinew, Szymon Myga

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引用次数: 0

摘要

我们扩展了 Lewicka - Pakzad, Sz\'ekelyhidi - Cao 和 Li - Qiuto 的方法，研究了复$sigma_2$方程在$mathbb C^n,\ n\geq 2$域中的极弱解的概念。作为副产品，我们提高了李和邱在实例中得到的反例的规律性临界值。

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Very weak solutions of quadratic Hessian equations

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

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arXiv - MATH - Complex Variables

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