A countable family of scaled exterior measurements of the fractional Schrödinger obstacle problem determines the nonnegative potential throughout the domain.
The Wiener criterion for nonlocal Dirichlet problems
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abstract
We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability $s \in (0, 1)$ and summability $p>1$. We establish a nonlocal counterpart of the Wiener criterion, which characterizes a regular boundary point in terms of the nonlocal nonlinear potential theory.
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An Inverse Obstacle Problem for the Fractional Schr\"odinger Equation
A countable family of scaled exterior measurements of the fractional Schrödinger obstacle problem determines the nonnegative potential throughout the domain.