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arXiv · 1710.05880

Extension and trace for nonlocal operators

Krzysztof Bogdan·Tomasz Grzywny·Katarzyna Pietruska-Pałuba·Artur Rutkowski
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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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Krzysztof Bogdan, Tomasz Grzywny, Katarzyna Pietruska-Pałuba, Artur Rutkowski. 2017-10-16. Extension and trace for nonlocal operators. https://arxiv.org/abs/1710.05880

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