Nonlinear Hodge maps

Details Nonlinear Hodge maps Nonlinear Hodge maps

1999-08-31

arxiv.org/abs/math-ph/9908030v6

J.Math.Phys. 41 (2000) 5745-5766

Physics

Mathematical Physics

Slightly modified and updated version; tcilatex, 32 pages

Scientific paper

10.1063/1.533436

We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models certain kinds of compressible flow. Conditions are found under which singular sets of prescribed dimension cannot occur. Various degrees of smoothness are proven for the sonic limit, high-dimensional flow, and flow having nonzero vorticity. The gradient flow of solutions is estimated. Implications for other quasilinear field theories are suggested.

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