Aspects of the $L^{2}$-Sobolev theory of the $\bar{\partial}$-Neumann problem

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107418The $\bar{\partial}$-Neumann problem is the fundamental boundary value problem in several complex variables. It features an elliptic operator coupled with non-coercive boundary conditions. The problem is globally regular on many, but not all, pseudoconvex domains. We discuss several recent developments in the $L^{2}$-Sobolev theory of the $\bar{\partial}$-Neumann problem that concern compactness and global regularity.Complex VariablesAnalysis of PDEs32W05; 35N15Aspects of the $L^{2}$-Sobolev theory of the $\bar{\partial}$-Neumann problemtext