Hölder estimates for homotopy operators on strictly pseudoconvex domains with C² boundary

2017/02/28 by Xianghong Gong, Gong, Xianghong
Computer Science · Mathematics · #32A06 #32T15 #32W05 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1702.08872

openalex publication_date 2017/02/28 · openalex created_date 2017/03/16 · openalex updated_date 2026/07/28

Abstract

We derive a new homotopy formula for a strictly pseudoconvex domain of C² boundary in \mathbf Cⁿ by using a method of Lieb and Range and obtain estimates in Lipschitz spaces for the homotopy operators. For r>1 and q>0, we obtain a Λ_r+1/2 solution u to ∂ u=f for ∂-closed (0,q) forms f of class Λ_r on the domain. We apply the estimates to obtain boundary regularities of \mathcal D-solutions for a domain in the Levi-flat Euclidean space.

Related

• Weighted Sobolev L^p estimates for homotopy operators on strictly pseudoconvex domains with C² boundary
• A universal ∂ solution operator on nonsmooth strongly pseudoconvex domains
• Sobolev and Hölder estimates for the ∂ equation on pseudoconvex domains of finite type in \mathbb C²
• On ∂ homotopy formulae for product domains: Nijenhuis-Woolf's formulae and optimal Sobolev estimates
• Exact regularity of ∂ on pseudoconvex domains in ℂ²