A sub-elliptic estimate for a class of invariantly defined elliptic systems
Copyright policy )A sub-elliptic estimate for a class of invariantly defined elliptic systems
We consider a certain invariantly defined nonlinear system of partial differential equations on a Riemannian manifold. Since a special case describes a steady, irrotional, compressible flow on the manifold, it is natural to refer to the (square of) the pointwise norm of the solution as the speed of the flow and to the density of the flow. Under appropriate restrictions on the density, the system is elliptic and we obtain a sub-elliptic estimate and a maximum principle for the speed of the flow in terms of the curvature of the manifold.
second order scalar elliptic equation, 76N15, Smoothness and regularity of solutions to PDEs, Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.), integration by parts techniques, 58G99, 35J99, Nonlinear elliptic equations, subsolution, maximum principle, non-linear elliptic system for p-forms, Riemannian geometry
second order scalar elliptic equation, 76N15, Smoothness and regularity of solutions to PDEs, Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.), integration by parts techniques, 58G99, 35J99, Nonlinear elliptic equations, subsolution, maximum principle, non-linear elliptic system for p-forms, Riemannian geometry
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