The \(\partial \)-Neumann operator on strongly pseudoconvex domain with piecewise smooth boundary. (English) Zbl 1108.35027

The paper deals with the \(\bar \partial \)-Neumann operator \(N\:L^2_{(r,q)}(D)\to L^2_{(r,q)}(D)\), if \(D\subset \mathbb C^n\) is a bounded strongly pseudoconvex domain with piecewise smooth boundary. The authors prove that it can be extended as a bounded operator from the Sobolev space \(H^{-1/2}_{(r,q)}(D)\) into \(H^{1/2}_{(r,q)}(D)\). In particular, \(N\) is a compact operator on \(L^2_{(r,q)}(D)\) and \(H^{-1/2}_{(r,q)}(D)\).


35F15 Boundary value problems for linear first-order PDEs
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
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