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Subelliptic estimates for the \(\overline\partial\)-Neumann operator on piecewise smooth strictly pseudoconvex domains. (English) Zbl 0953.32027

It is shown that the \(\overline \partial \)-Neumann operator \(N\) satisfies subelliptic estimates on a domain with piecewise smooth strictly pseudoconvex boundary, more precisely, it is shown that \(N\) maps \(L^2_{(p,q)}(\Omega)\) into \(H^{1/2}_{(p,q)}(\Omega)\) when \(1\leq q \leq n-1.\)
Moreover the authors prove that \(\overline \partial N\) and \(\overline \partial * N\) have the same properties.
It is also indicated that subellipticity does not imply regularity in other Sobolev spaces in this case, in contrast to smooth domains [J. J. Kohn and L. Nirenberg, Commun. Pure Appl. Math. 18, 443-492 (1965; Zbl 0125.33302)].
Reviewer: F.Haslinger (Wien)

MSC:

32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
35N15 \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs

Citations:

Zbl 0125.33302
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References:

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