DOCUMENTA MATHEMATICA, Extra Volume ICM II (1998), 627-636

Michael Christ

Title: Singularity and Regularity --- Local and Global

There exists a smoothly bounded, pseudoconvex domain in $\complex^2$ 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.

1991 Mathematics Subject Classification: 32F20, 35N15, 35P30, 42B99

Keywords and Phrases: Hypoellipticity, global regularity, Bergman projection, $\bar\partial$--Neumann problem.

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