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Title: Critical O(d)-equivariant biharmonic maps
Contributor(s): Cooper, Matthew K  (author)
Publication Date: 2015
Open Access: Yes
DOI: 10.1007/s00526-015-0888-0Open Access Link
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Abstract: We study O(d)-equivariant biharmonic maps in the critical dimension. A major consequence of our study concerns the corresponding heat flow. More precisely, we prove that blowup occurs in the biharmonic map heat flowfrom B⁴(0, 1) into S⁴. To our knowledge, this was the first example of blowup for the biharmonic map heat flow. Such results have been hard to prove, due to the inapplicability of the maximum principle in the biharmonic case. Furthermore, we classify the possible O(4)-equivariant biharmonic maps from R⁴ into S⁴, and we show that there exists, in contrast to the harmonic map analogue, equivariant biharmonic maps from B⁴(0, 1) into S⁴ that wind around S⁴ as many times as we wish. We believe that the ideas developed herein could be useful in the study of other higher-order parabolic equations.
Publication Type: Journal Article
Grant Details: ARC/DP120101886
Source of Publication: Calculus of Variations and Partial Differential Equations, 54(3), p. 2895-2919
Publisher: Springer
Place of Publication: Heidelberg, Germany
ISSN: 0944-2669
Field of Research (FOR): 010102 Algebraic and Differential Geometry
010110 Partial Differential Equations
010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
Socio-Economic Outcome Codes: 970101 Expanding Knowledge in the Mathematical Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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