Seminario Dottorato: L^2 theory and global regularity for d-bar on pseudoconvex domains of C^n

Wednesday 16 November 2011 - Stefano Pinton

ARGOMENTI: Seminari Dottorato

Wednesday 16 November 2011 h. 16:00, room 2BC30
Stefano Pinton (Dip. Mat.)
"L^2 theory and global regularity for d-bar on pseudoconvex domains of C^n"

This seminar is divided into two parts. The first one is an introduction to the first order partial differential operator d-bar in a smooth bounded pseudoconvex domain D of C^n. Only preliminary definitions are given and the basic estimate, due to Morrey, Kohn and Hormander, is established. It yields the existence of the d-bar Neumann operator, that is, the inverse to the complex Laplacian and the construction of the canonical solution to the equation di-bar(u)=f, for f in Ker(di-bar), that is the solution orthogonal to the Kernel of d-bar. The second part is an introduction to the problem of the global regularity up to the boundary for the canonical solution of the d-bar equation with data regular up to the boundary. In particular it is shown how compactness estimates are sufficient for global regularity as well as the existence of "good defining functions".

Rif. int. C. Marastoni, T. Vargiolu

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