Singularity and regularity – local and global. (English) Zbl 0913.32003

Christ, Michael

Doc. Math., Extra Vol. ICM Berlin 1998, vol. II, 627-636 (1998).

We quote the author’s abstract: “There exists a smoothly bounded, pseudo-convex domain in \(\mathbb{C}^2\) for which the Bergman projection fails to preserve the class of functions which are globally smooth up to the boundary. The counterexample is explained and placed in a wider context through a broader discussion of the local and global regularity of solutions to subelliptic and more degenerate partial differential equations in various function spaces”.

Reviewer: E.J.Straube (College Station)

MSC:

32W05	\(\overline\partial\) and \(\overline\partial\)-Neumann operators
35N15	\(\overline\partial\)-Neumann problems and formal complexes in context of PDEs
35P30	Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
42B99	Harmonic analysis in several variables

Keywords:

hypoellipticity; \(\overline\partial\)-Neumann problem; Bergman projection; global regularity