## 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

Zbl 0125.33302
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### References:

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