Fractional analogue of k-Hessian operators

Yijing Wu

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arxiv 1709.02550 v1 pith:5UYPQZ6A submitted 2017-09-08 math.AP

Fractional analogue of k-Hessian operators

Yijing Wu This is my paper

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keywords fractionalanalogueoperatorsglobalk-hessianoperatorprovesolutions

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Applying ideas of fractional analogue of Monge-Amp\'ere operator by L. Caffarelli and F. Charro, we consider an analogue of fractional k-Hessian operators expressed as concave envelopes of fractional linear operators, and reproduce the same regularity results when k=2. Under the set up of global solutions prescribing data at infinity and global barriers, the key estimate is to prove that fractional 2-Hessian operator is strictly elliptic. Then we can apply nonlocal Evans-Krylov theorem to prove such solutions are classical.

Fractional analogue of k-Hessian operators

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