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An inverse mapping theorem for Sobolev chains and its application

Published online by Cambridge University Press:  17 April 2009

Truong Công Nghê
Truong Công Nghê
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales 2006, Australia.
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Abstract

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The author combines the methods used by Yamamuro and Omori to define a differentiation in Sobolev chains and obtain an Inverse Mapping Theorem. He then uses this theorem to give a new proof for a result of Sunada on the local finite-dimensionality of the solution space of a non-linear elliptic differential operator with smooth coefficients.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 3 , June 1983 , pp. 381 - 394
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Kuranishi, M., “A new proof for regularity of solutions of elliptic differential operators”, Global analysis and its applications, Vol. II, 355–361 (Lectures, Internat. Sem. Course, Internat. Centre Theoret. Phys., Trieste, 1972. International Atomic Energy Agency, Vienna, 1974).Google Scholar
[2]Narasimhan, Reghavan, Analysis on real and complex manifolds (Advanced Studies in Pure Mathematics, 1. Masson, Paris; North-Holland, Amsterdam; 1973).Google Scholar
[3]Omori, Hideki, Infinite dimensional Lie transformation groups (Lecture Notes in Mathematics, 427. Springer-Verlag, Berlin, Heidelberg, New York, 1974).CrossRefGoogle Scholar
[4]Palais, R.S., “Differential operators on vector bundles”, Seminar on the Atiyah-Singer index theorem, 51–93 (Princeton University Press, Princeton, New Jersey, 1965).Google Scholar
[5]Palais, Richard S., Foundation of global non-linear analysis (Benjamin, New York, Amsterdam, 1968).Google Scholar
[6]Sunada, Toshikazu, “Non-linear elliptic operators on a compact manifold and an implicit function theorem”, Nagoya Math. J. 56 (1974), 175–200.CrossRefGoogle Scholar
[7]Yamamuro, Sadayuki, A theory of differentiation in locally convex spaces (Memoirs of the American Mathematical Society, 212. American Mathematical Society, Providence, Rhode Island, 1979).Google Scholar
[8]Yamamuro, Sadayuki, “A note on Omori-Lie groups”, Bull. Austral. Math. Soc. 19 (1978), 333–349.CrossRefGoogle Scholar