On a bounded Lipschitz domain, a sequence with bounded norms and bounded total variation seminorm has a subsequence converging strongly in . The limit is in the BV space, and its variation does not exceed the limit inferior. This supplies the compactness step of the direct method in the calculus of variations for linearly growing gradient energies.

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  1. Function of bounded variation on a domain
  2. Total variation seminorm on a domain
  3. Variational regularization
  4. Regularization of an inverse problem
  5. Inverse problem
  6. Analysis
  7. Area of mathematics
  8. Mathematics
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