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Non-Uniqueness for the p-Harmonic Flow

Published online by Cambridge University Press:  20 November 2018

Norbert Hungerbühler
Norbert Hungerbühler*
Affiliation:
ETH-Zentrum Departement Mathematik CH-8092 Zürich Switzerland, e-mail: [email protected]
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Abstract

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If f0: Ω ⊂ ℝm → Sn is a weakly p-harmonic map from a bounded smooth domain Ω in ℝm (with 2 < p < m) into a sphere and if f0 is not stationary p-harmonic, then there exist infinitely many weak solutions of the p-harmonic flow with initial and boundary data f0, i.e., there are infinitely many global weak solutions f :Ω × ℝ → ⊂ Sn of

We also show that there exist non-stationary weakly (m − 1)-harmonic maps f0: Bm → Sm−1.

Keywords

35K4035K5535K65
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 2 , 01 June 1997 , pp. 174 - 182
Copyright
Copyright © Canadian Mathematical Society 1997

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