Optimal Sobolev regularity of ∂ on the Hartogs triangle

2022/10/06 by Yifei Pan, Yuan Zhang, Pan, Yifei +1
Mathematics · #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2210.02619

Abstract

In this paper, we show that for each k∈ \mathbb Z⁺, p>4, there exists a solution operator \mathcal T_k to the ∂ problem on the Hartogs triangle that maintains the same W^{k, p} regularity as that of the data. According to a Kerzman-type example, this operator provides solutions with the optimal Sobolev regularity.

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