## 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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