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On a Fractional Monge–Ampère Operator
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
doi:10.1007/s40818-015-0005-x
fatcat:2xg6atmbz5duthspnduon37xeq