The obstacle problem for integral diffusions

Luis Caffarelli (University of Texas at Austin, USA)

Plan of the course

1. Non local diffusions
2. Fractional diffusions as a Dirichlet to Neumann map
3. The obstacle problem for fractional diffusions: optimal regularity, free boundary regularity.

The course will be based on the preprints

• L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian.
• I. Athanasopoulos, L. A. Caffarelli, and S. Salsa, The structure of the free boundary for lower dimensional obstacle problems.
• L. A. Caffarelli, S. Salsa, and L. Silvestre, Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian.