Global Subjectivity of Submersions via Contractibility of the Fibers
Abstract
We give sufficient condition for a C(1) submersion F : X - Y, X Y real Banach spaces, to be surjective with contractible fibers F(-1)(y). Roughly speaking, this condition "interpolates" two well-known but unrelated hypotheses coresponding to the two extreme cases: Hadanard's criterion when Y = X and F is a local diffeomorphism, and the Palais-Smale condition when Y = R. These results may be viewed as a global variant of the implicit function theorem, which unlike the local one does not require split kernels. They are derived form a deformation theorem tailored to fit functionals with a norm-like nondifferentiability.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 07, 1994
- Accession Number
- ADA284961
Entities
People
- Patrick J. Rabier
Organizations
- University of Pittsburgh