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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