The infimum of over is attained. A minimizing sequence is bounded in because is bounded below; weak compactness, Rellich strong convergence, and weak lower semicontinuity complete the direct-method argument.

Ancestors (10)

  1. Weak lower semicontinuity of a bounded-domain Schrodinger energy
  2. Rellich-Kondrashov compactness theorem for H01
  3. Rellich-Kondrachov compactness theorem
  4. Sobolev embedding theorem
  5. Sobolev space
  6. Functional analysis
  7. Analysis
  8. Area of mathematics
  9. Mathematics
  10. Home

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