| Abstract: |
| We introduce the fractional normal derivative of a function on the boundary of a bounded domain as the fractional power of the Dirichlet-to-Neumann map for its corresponding harmonic extension to the interior. We prove Holder regularity estimates of solutions to the boundary nonlocal problem depending on the regularity of the boundary manifold. This is joint work with Luis A. Caffarelli (UT Austin) and Mitchell Haeuser (Iowa State University). |
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