An important question in complex analysis is to solve the inhomogenous Cauchy-Riemann equations (also called the d-bar equation) in a domain in C^n. The question of boundary smoothness in the d-bar problem is classically dealt with by solving the associated d-bar Neumann problem and showing that the solution operator, the $\\overline{\\partial}$-Neumann operator is compact. For many domains of interest, in particular the product domains, this approach fails. We discuss in this talk some new results on the regularity of the d-bar problem in product domains. This work is joint with Mei-Chi Shaw.

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Last updated: 04 Aug 2020