A universal ∂ solution operator on nonsmooth strongly pseudoconvex domains

2024/12/29 by Liding Yao, Yao, Liding
Computer Science · Mathematics · #32A26 (primary) 32T25 #32W05 and 46E35 (secondary) #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2412.20312

openalex publication_date 2024/12/29 · openalex created_date 2025/01/01 · openalex updated_date 2026/07/28

Abstract

We construct homotopy formulae f=∂ \mathcal H_q f+\mathcal H_q+1∂ f on a bounded domain which is either C² strongly pseudoconvex or C^1,1 strongly \mathbb C-linearly convex. Such operators exhibit Sobolev estimates \mathcal H_q:H^s,p→ H^s+1/2,p and Hölder-Zygmund estimates \mathcal H_q:\mathscr C^s→\mathscr C^s+1/2 simultaneously for all s∈\mathbb R and 1

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