Density problems on vector bundles and manifolds. (English) Zbl 1310.46032
Summary: We study some canonical differential operators on vector bundles over smooth, complete Riemannian manifolds. Under very general assumptions, we show that smooth, compactly supported sections are dense in the domains of these operators. Furthermore, we show that smooth, compactly supported functions are dense in second order Sobolev spaces on such manifolds under the sole additional assumption that the Ricci curvature is uniformly bounded from below.
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
| 58J60 | Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) |
Keywords:
density problems; first-order operators on vector bundles; Laplacian on vector bundles; second-order Sobolev spaces on manifoldsReferences:
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