q-Pseudoconvexity and Regularity at the Boundary for Solutions of the \bar \partial -problem |
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Authors: | Giuseppe Zampieri |
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Institution: | (1) Dip. Matematica-Universitè, v. Belzoni 7, Padova, Italy |
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Abstract: | For a domain of
we introduce a fairly general and intrinsic condition of weak q-pseudoconvexity, and prove, in Theorem 4, solvability of the
-complex for forms with
-coefficients in degree
. All domains whose boundary have a constant number of negative Levi eigenvalues are easily recognized to fulfill our condition of q-pseudoconvexity; thus we regain the result of Michel (with a simplified proof). Our method deeply relies on the L
2-estimates by Hörmander (with some variants). The main point of our proof is that our estimates (both in weightened-L
2 and in Sobolev norms) are sufficiently accurate to permit us to exploit the technique by Dufresnoy for regularity up to the boundary. |
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Keywords: | Cauchy– Riemann system L
2-estimates |
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