On a Fractional Monge–Ampère Operator

Luis Caffarelli, Fernando Charro
2015 Annals of PDE  
In this paper we consider a fractional analogue of the Monge-Ampère operator. Our operator is a concave envelope of fractional linear operators of the form _A∈AL_Au, where the set of operators corresponds to all affine transformations of determinant one of a given multiple of the fractional Laplacian. We set up a relatively simple framework of global solutions prescribing data at infinity and global barriers. In our key estimate, we show that the operator remains strictly elliptic, which allows
more » ... to apply known regularity results for uniformly elliptic operators and deduce that solutions are classical.
doi:10.1007/s40818-015-0005-x fatcat:2xg6atmbz5duthspnduon37xeq