Exact regularity of the ∂-problem with dependence on the ∂_b-problem on weakly pseudoconvex domains in ℂ²

2014/06/28 by Ehsani, Dariush
#32W05 #32W10 #32W25 #32W50 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1406.7381

Abstract

We reduce the problem of constructing a linear solution operator to the ∂-equation on smoothly bounded weakly pseudoconvex domains, Ω, in ℂ² to the problem of the boundary ∂_b-equation. We show there is a solution operator to ∂ which is bounded as a map W^s_(0,1)(Ω)∩ker ∂ → W^s(Ω) for all s≥ 0 if there is a corresponding solution operator to the ∂_b-problem with analogous regularity properties.

Related

• Exact regularity of ∂ on pseudoconvex domains in ℂ²
• The ∂-equation on variable strictly pseudoconvex domains
• Sobolev regularity of the canonical solutions to ∂ on product domains
• Weighted estimates for the \\∂-Neumann problem on\n intersections of strictly pseudoconvex domains in \ℂ²
• Optimal Hölder regularity for the ∂ problem on product domains in \mathbb C²