Resumen de A bounded linear extension operator for L2,p(R2)

Arie Israel

• Let L2,p(R2) be the Sobolev space of real-valued functions on the plane whose Hessian belongs to Lp. For any finite subset E?R2 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.