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The L2--problem on manifolds with piecewise strictly pseudoconvex boundaries

Published online by Cambridge University Press:  24 October 2008

Patrick W. Darko
Patrick W. Darko
Affiliation:
Department of Mathematics, University of Ghana, P.O. Box 62, Legon, Ghana
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Extract

Ever since the solution of the -Neumann problem by Kohn [4], refinements, extensions and estimates of the solution have been made by a lot of people up to the present day. Kohn discovered that, where the -Neumann problem was solvable, the space of harmonic forms is finite dimensional and it followed from Hörmander's solution [3] that on bounded pseudoconvex domains in ℂn the appropriate spaces of harmonic forms are zero dimensional.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 1 , July 1994 , pp. 147 - 149
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

REFERENCES

[1]Andreotti, A. and Hill, C. Denson. Levi, E. E.convexity and Hans Lewy Problem Part II. Vanishing Theorems. Annali della Scuola Normale Superiore de Pisa, Classe di Scienze, Vol. xxvi Fasc. iv (1972), 747–806.Google Scholar
[2]Andreotti, A. and Grauert, H.. Théorème de finitude pour Ia Cohomologie des espaces complexes. Bull. Soc. Math. France 90 (1962), 193–259.CrossRefGoogle Scholar
[3]Hörmander, L.. L 2 estimates and existence theorems for the -operator. Acta Math. 113 (1965), 89–152.CrossRefGoogle Scholar
[4]Kohn, J. J.. Harmonic integrals on strongly pseudoconvex manifolds. I. Ann. of Math. 78 (1963), 1122–1148CrossRefGoogle Scholar
Kohn, J. J.. Harmonic integrals on strongly pseudoconvex manifolds. II. Ann. of Math. 79 (1964), 450–472.CrossRefGoogle Scholar
[5]Kerzman, N.. Hölder and L p estimates for solutions of in strongly pseudoconvex domains. Comm. Pure Appl. Math. 24 (1971), 301–379.CrossRefGoogle Scholar
[6]Range, R. M. and Siu, Y. T.. Uniform estimates for the -equation on domains with piecewise smooth pseudoconvex boundaries. Math. Ann. 206 (1973), 325–354.CrossRefGoogle Scholar