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Antonio Greco
Fractional convexity maximum principle
(208K, pdf)

ABSTRACT.  We construct an anisotropic, degenerate, fractional operator that nevertheless satisfies a strong form of the maximum principle. By applying such an operator to the concavity function associated to the solution of an equation involving the usual fractional Laplacian, we obtain a fractional form of the celebrated convexity maximum principle devised by Korevaar in the 80's. Some applications are discussed.