Extension and trace for nonlocal operators
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2017
- DOI:
- 10.48550/arXiv.1710.05880
- arXiv:
- arXiv:1710.05880
- Bibcode:
- 2017arXiv171005880B
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematics - Probability;
- 46E35 (Primary);
- 35A15;
- 31C05 (Secondary)
- E-Print:
- We are now able to add the trace theorem and complete the picture