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On the Continuity of Exterior Differentiation Between Sobolev-Slobodeckij Spaces of Sections of Tensor Bundles on Compact Manifolds
Ali Behzadan
UCSD
Abstract:
Suppose Ω is a nonempty open set with Lipschitz continuous boundary in \mathbbRn. There are certain exponents e ∈ R and q ∈ (1,∞) for which [(∂)/(∂xj)]: We,q(Ω)→ We−1,q(Ω) is NOT a well-defined continuous operator. Now suppose M is a compact smooth manifold. In this talk we will try to discuss the following questions:
1. How are Sobolev spaces of sections of vector bundles on M defined?
2. Is it possible to extend d: C∞(M)→ C∞(T*M) to a continuous linear map from We,q(M) to We−1,q(T*M) for all e ∈ R and q ∈ (1,∞)?
3. Why are we interested in the above question?
Tuesday, May 9, 2017
11:00AM AP&M 2402
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Randolph E. Bank
Philip E. Gill
Michael Holst
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Randolph E. Bank
Philip E. Gill
Michael Holst
Administrative Contact:
[ Click to Send Email ]
Ali Behzadan
UCSD
Abstract:
Suppose Ω is a nonempty open set with Lipschitz continuous boundary in \mathbbRn. There are certain exponents e ∈ R and q ∈ (1,∞) for which [(∂)/(∂xj)]: We,q(Ω)→ We−1,q(Ω) is NOT a well-defined continuous operator. Now suppose M is a compact smooth manifold. In this talk we will try to discuss the following questions:
1. How are Sobolev spaces of sections of vector bundles on M defined?
2. Is it possible to extend d: C∞(M)→ C∞(T*M) to a continuous linear map from We,q(M) to We−1,q(T*M) for all e ∈ R and q ∈ (1,∞)?
3. Why are we interested in the above question?
Tuesday, May 9, 2017
11:00AM AP&M 2402