Abstract
We consider inequalities of the form ∝ ∂Ω u 2 ds ⩽ C ∝ Ω (u 2 + u, iu i) d x ( ∗) for sufficiently regular functions u(x) defined on a bounded domain Ω in R n . The inequality ( ∗) follows from the Trace Theorem in interpolation spaces and so is called a trace inequality. Information on the optimal constants C (which depend on the domain geometry) is obtained through consideration of associated eigenvalue problems.
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