The sliding method for the nonlocal Monge–Ampère operator. (July 2020) - Chen, Xueying; Bao, Gejun; Li, Guanfeng
Abstract: We develop a sliding method for the nonlocal Monge–Ampère operator. We first establish a narrow region principle in bounded domains, which plays an important role in the sliding method. Then we consider the equation with the nonlocal Monge–Ampère operator and derive the monotonicity of solutions in both bounded domains and the whole space. We use a new idea-estimating the singular integrals defining the nonlocal Monge–Ampère operator along a sequence of approximate maximum points.