We prove existence, uniqueness and optimal regularity of solutions to the stationary obstacle problem defined by the fractional Laplacian operator with drift, in the subcritical regime. As in , we localize our problem by considering a suitable extension operator introduced in . The structure of the extension equation is different from the one constructed in , in that the obstacle function has less regularity, and exhibits some singularities. To take into account the new features of the problem, we prove a new monotonicity formula, which we then use to establish the optimal regularity of solutions.
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- Almgren-type monotonicity formula
- Fractional Laplacian with drift
- Obstacle problem
- Optimal regularity