Very weak solutions of quadratic Hessian equations

We extend the methods of Lewicka - Pakzad, Székelyhidi - Cao and Li - Qiu to study the notion of very weak solutions to the complex $σ_2$ 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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Publication Details

Journal
Nonlinear Analysis
Published
2026-07-24
DOI
https://doi.org/10.1016/j.na.2026.114236
Primary Topic
Geometric Analysis and Curvature Flows
Type
article
Field-Weighted Citation Impact
0.00

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article

Very weak solutions of quadratic Hessian equations

Sławomir Dinew, Szymon Myga
Nonlinear Analysis
Geometric Analysis and Curvature Flows
article

Very weak solutions of quadratic Hessian equations

Sławomir Dinew, Szymon Myga
article en

Abstract

We extend the methods of Lewicka - Pakzad, Székelyhidi - Cao and Li - Qiu to study the notion of very weak solutions to the complex $σ_2$ 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.

Nonlinear AnalysisVol. 274
Narodowe Centrum Nauki
Openalex Percentile: Top 98%
Geometric Analysis and Curvature Flows
DOIOpen Access PDFOpenAlex
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Very weak solutions of quadratic Hessian equations — Sławomir Dinew, Szymon Myga · Nonlinear Analysis (2026) | TGRS Research Map | TGRS