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

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”.

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
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