Luke Rogers (Stony Brook/Cornell University)
A degree-independent Sobolev embedding theorem
Abstract.
Building on work of Calderon, Stein and Jones, we construct a degree-independent operator which extends Sobolev functions from a locally uniform domain to Euclidean space. Extension operators that depend on the degree of (weak) differentiability of the functions were already known (due to Calderon for Lipschitz domains and Jones for locally uniform domains). Stein gave a degree-independent operator for Lipschitz domains, and it is a modification of his approach that we generalize to locally uniform domains.

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