## 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 $$H^{-1/2}_{(r,q)}(D)$$.

### MSC:

 35F15 Boundary value problems for linear first-order PDEs 32W05 $$\overline\partial$$ and $$\overline\partial$$-Neumann operators
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### References:

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