Conservation laws for fourth order systems in four dimensions

Lamm, Tobias; Riviere, Tristan

doi:10.1080/03605300701382381

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Conservation laws for fourth order systems in four dimensions

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Lamm, Tobias
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;
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Citation

Lamm, T., & Riviere, T. (2008). Conservation laws for fourth order systems in four dimensions. Communications in Partial and Differential Equations, 33(2), 245-262. doi:10.1080/03605300701382381.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-628D-3

Abstract

Following an approach of the second author for conformally invariant variational problems in two dimensions, we show in four dimensions the existence of a conservation law for fourth order systems, which includes both intrinsic and extrinsic biharmonic maps. With the help of this conservation law we prove the continuity of weak solutions of this system. Moreover we use the conservation law to derive the existence of a unique global weak solution of the extrinsic biharmonic map flow in the energy space.