Optimal Hölder Regularity of Solution Operator to the ∂-equation on Product Domains

2022/04/16 by Yu Jun Loo, Loo, Yu Jun
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2204.07690

openalex publication_date 2022/04/16 · openalex created_date 2022/04/26 · openalex updated_date 2026/07/28

Abstract

This note seeks to prove the existence of a canonical solution operator to the ∂-equation that preserves Hölder regularity on product domains. It is a well known fact that such solution operators do not in general gain Hölder regularity, and as such, our solution operator is optimal in this regard.

Related

• Hölder regularity of the ∂-equation on the polydisc
• Optimal Hölder regularity for the ∂ problem on product domains in \mathbb C²
• Sobolev regularity of the canonical solutions to ∂ on product domains
• Uniform estimates for the canonical solution to the ∂-equation on product domains
• Hölder estimates for the ∂ problem for (p,q) forms on product domains