Sharp Boundary Trace Inequalities
نویسنده
چکیده
This paper describes sharp inequalities for the trace of Sobolev functions on the boundary of a bounded region Ω ⊂ R . The inequalities bound (semi-)norms of the boundary trace by certain norms of the function and its gradient on the region and two specific constants kρ and kΩ associated with the domain and a weight function. These inequalities are sharp in that there are functions for which equality holds. Explicit inequalities in some special cases when the region is a ball, or the region between two balls, are evaluated.
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