Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Compact embedding and strong convergence

  1. Aug 4, 2010 #1
    Let X be compactly embedded in Y. Assume also that
    there is a sequence f_n in X such that
    f_n converges to f weakly in X and strongly in Y to some function f in X.
    Can we say that f_n converges to f strongly in X?
     
  2. jcsd
  3. Aug 6, 2010 #2
    Yes, it's due to the compactness of the embedding.
     
  4. Aug 21, 2010 #3
    Which assumption together with compactness imply this? Weak convergence in X or strong convergence in Y or both? Could you elaborate more?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Compact embedding and strong convergence
  1. Converges to (Replies: 1)

Loading...