Solving the Kerzman's problem on the sup-norm estimate for ∂ on product domains

2023/07/11 by Song-Ying Li, Li, Song-Ying
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2307.04951

openalex publication_date 2023/07/11 · openalex created_date 2023/07/13 · openalex updated_date 2026/07/28

Abstract

In this paper, the author solves the long term open problem of Kerzman on sup-norm estimate for Cauchy-Riemann equation on polydisc in n-dimensional complex space. The problem has been open since 1971. He also extends and solves the problem on a bounded product domain Ωⁿ, where Ω is any bounded domain in ℂ with C^1,α boundary for some α>0.

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