Remarks on weakly stationary maps into spheres characterized by wedge product
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In Chen (Math Z 201:69–74, 1989, Math Z 215:25–35, 1994), Chen first used the wedge product for weak solutions of the harmonic map flow and the p-harmonic one into the spheres. The notion of the wedge product is useful in studying such weak solutions into the spheres. In this paper we consider weak solutions of systems of more general differential equations. Furthermore we clarify an essential structure of general systems of equations necessary for an application of wedge product.
KeywordsElliptic system Wedge product Weak solution Sphere Harmonic map Symphonic map
Mathematics Subject ClassificationPrimary Secondary: 58E99 58E20 53C43
This work was partially supported by the Grant-in-Aid for Scientific Research (C) No.15K04962 (Misawa) and No.15K04846 (Nakauchi) at Japan Society for the Promotion of Science.