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Some Properties of the Degree for a Class of Sobolev Maps

Christoph Hamburger
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 455, No. 1986 (Jun. 8, 1999), pp. 2331-2349
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/53327
Page Count: 19
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Some Properties of the Degree for a Class of Sobolev Maps
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Abstract

We prove that a map u ∈ Wloc1,1( M, N), whose differential and adjoint are integrable with exponents n - 1 ≤ p ≤ n and n/(n - 1)≤ q < ∞ respectively, possesses an integer valued degree with the usual properties. Here M∈ C0,1 and N∈ C1,1 are n-dimensional oriented Riemannian manifolds, with ∂ M possibly non-empty.

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