Abstract
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 [4], we localize our problem by considering a suitable extension operator introduced in [2]. The structure of the extension equation is different from the one constructed in [4], 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.
Original language | English (US) |
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Pages (from-to) | 417-472 |
Number of pages | 56 |
Journal | Journal of Functional Analysis |
Volume | 268 |
Issue number | 2 |
DOIs | |
State | Published - Jan 15 2015 |
Bibliographical note
Publisher Copyright:© 2014 Elsevier Inc.
Keywords
- Almgren-type monotonicity formula
- Fractional Laplacian with drift
- Obstacle problem
- Optimal regularity