Very weak solutions of quadratic Hessian equations

2024/09/13 by Sławomir Dinew, Szymon Myga, Dinew, Sławomir +1
#math.AP #math.CV

paper · pdf · doi:10.48550/arxiv.2409.08852

Abstract

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

Citations

• The Monge-Ampère system in dimension two: A regularity improvement
• Very weak solutions of the Dirichlet problem for the two dimensional Monge-Ampère equation
• Viscosity solutions to complex Hessian equations
• On the definition of the Monge-Amp�re operator in ?2
• Quasiconvex Functions and Hessian Equations
• A construction of inner functions on the unit ball inC p
• Fonctions holomorphes bornees sur la boule unite deC n

Related

• The weak solutions to complex Hessian equations
• Very weak solutions of the Dirichlet problem for 2-Hessian equation
• Remarks on the quadratic Hessian equation
• Hessian estimate for semiconvex solutions to the sigma-2 equation
• Non-polynomial entire solutions to σ_k equations