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math.AP2007★ 614 cited
Regularity theory for fully nonlinear integro-differential equations
Luis Caffarelli, Luis Silvestre
We consider nonlinear integro-differential equations, like the ones that arise from stochastic control problems with purely jump Lèvy processes. We obtain a nonlocal version of the…
math.AP2007★ 555 cited
Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian
Luis Caffarelli, Sandro Salsa, Luis Silvestre
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equival…