Extension and trace for nonlocal operators

Published 16 Oct 2017 in math.AP and math.PR | (1710.05880v2)

Abstract: We prove an optimal extension and trace theorem for Sobolev spaces of nonlocal operators. The extension is given by a suitable Poisson integral and solves the corresponding nonlocal Dirichlet problem. We give a Douglas-type formula for the quadratic form of the Poisson extension.

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