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Biharmonic wave maps into spheres


Authors: Sebastian Herr, Tobias Lamm and Roland Schnaubelt
Journal: Proc. Amer. Math. Soc. 148 (2020), 787-796
MSC (2010): Primary 35L75, 58J45
DOI: https://doi.org/10.1090/proc/14744
Published electronically: August 7, 2019
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Abstract: A global weak solution of the biharmonic wave map equation in the energy space for spherical targets is constructed. The equation is reformulated as a conservation law and solved by a suitable Ginzburg-Landau-type approximation.


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Additional Information

Sebastian Herr
Affiliation: Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31, 33501 Bielefeld, Germany
Email: herr@math.uni-bielefeld.de

Tobias Lamm
Affiliation: Department of Mathematics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
Email: tobias.lamm@kit.edu

Roland Schnaubelt
Affiliation: Department of Mathematics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
Email: schnaubelt@kit.edu

DOI: https://doi.org/10.1090/proc/14744
Keywords: Global weak solutions, geometric plate equation, conservation law
Received by editor(s): December 10, 2018
Received by editor(s) in revised form: June 24, 2019
Published electronically: August 7, 2019
Additional Notes: The second and third author gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173.
Communicated by: Joachim Krieger
Article copyright: © Copyright 2019 American Mathematical Society