The obstacle problem for nonlinear integro-differential operators

Abstract

We investigate the obstacle problem for a class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional $p$-Laplacian operator with measurable coefficients. Amongst other results, we will prove both the existence and uniqueness of the solutions to the obstacle problem, and that these solutions inherit regularity properties, such as boundedness, continuity and Hölder continuity (up to the boundary), from the obstacle.

to appear in Calc. Var. Partial Differential Equations

References in corpus (3)

• Obstacle problems for integro-differential operators: Regularity of solutions and free boundaries
• 3-Commutators Estimates and the Regularity of 1/2 Harmonic Maps into Spheres
• Hölder estimates for viscosity solutions of equations of fractional $p$-Laplace type