文摘
It is proved that Green’s functions associated to the linearized Monge–Ampère operator satisfy certain Sobolev-type estimates within the natural first-order calculus. Our main result extends the classical Sobolev estimates for Green’s functions due to Grüter and Widman (Manuscr Math 37(3):303–342, 1982) in the uniformly elliptic case and it addresses a question posed by Le (Manuscr Math 149:45–62, 2016) in the degenerate and/or singular Monge–Ampère setting.