Subelliptic estimates for the \(\overline\partial\)-Neumann operator on piecewise smooth strictly pseudoconvex domains
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 [\textit{J. J. Kohn} and \textit{L. Nirenberg}, Commun. Pure Appl. Math. 18, 443-492 (1965; Zbl 0125.33302)].
\(\overline \partial \)-Neumann operator
piecewise smooth strictly pseudoconvex domains
scientific article; zbMATH DE number 1425116
scientific article