A bounded linear extension operator for L2.p(R2)

Abstract

Let L2;p(R2) be the Sobolev space of real-valued functions on the plane whose Hessian belongs to Lp;p. For any finite subset E ≈ R2;p and p > 2, let L2;p(R2)|E be the space of real-valued functions on E, equipped with the trace seminorm. In this paper we construct a bounded linear extension operator T : L2;p(R2)|E → L2;p(R2) We also provide an explicit formula that approximates the L2;p(R2)|E trace seminorm. © 2013 Department of Mathematics, Princeton University.