Equivalence of Sobolev Spaces
Copyright policy )Equivalence of Sobolev Spaces
The paper contains the proof that certain \(L^2\)-Sobolev spaces on Riemannian manifolds with bounded curvature of all orders are equivalent. The main idea is to find suitable commutator estimates. Moreover the method is extended to Dirac-type operators. Under the assumption on the weight it is used to extend to prove the equivalence of weighted Sobolev spaces.
- Aarhus University Denmark
Elliptic equations on manifolds, general theory, Asymptotic behavior of solutions to PDEs, Sobolev spaces, Bochner Laplacians, Dirac operators, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, manifolds with bounded curvature
Elliptic equations on manifolds, general theory, Asymptotic behavior of solutions to PDEs, Sobolev spaces, Bochner Laplacians, Dirac operators, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, manifolds with bounded curvature
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