Fractional infinity Laplacian with obstacle

Key Points

• The research aims to prove the existence of solutions for the obstacle problem associated with the fractional infinity Laplacian.
• Analyzed the obstacle problem with a nonhomogeneous term and boundary conditions.
• Utilized an approximation of the function to establish existence of solutions using Perron's method.
• Demonstrated uniform H"older estimates on approximated solutions.
• Existence of a solution $u$ is established under specified conditions for function $f$ and boundary datum $g$.
• The solution $u$ is shown to be $eta$-H"olderian on the closure of the domain $ar{\\Omega}$, indicating regularity in the solution.