Extension and trace for nonlocal operators

Artur Rutkowski; Katarzyna Pietruska-Pa{\l}uba; Krzysztof Bogdan; Tomasz Grzywny

arxiv: 1710.05880 · v2 · pith:2FZMHOHCnew · submitted 2017-10-16 · 🧮 math.AP · math.PR

Extension and trace for nonlocal operators

Krzysztof Bogdan , Tomasz Grzywny , Katarzyna Pietruska-Pa{\l}uba , Artur Rutkowski This is my paper

classification 🧮 math.AP math.PR

keywords extensionnonlocaloperatorspoissontracecorrespondingdirichletdouglas-type

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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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Extension and trace for nonlocal operators

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