Fractional convexity
نویسندگان
چکیده
We introduce a notion of fractional convexity that extends naturally the usual in Euclidean space to setting. With this convexity, we study convex envelope inside domain an exterior datum (the largest possible function is below outside) and show characterized as viscosity solution non-local equation given by infimum among all directions 1-dimensional laplacian. For prove existence, uniqueness comparison principle (in framework solutions). In addition, find solutions for are related Monge–Ampere equation.
منابع مشابه
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2021
ISSN: ['1432-1807', '0025-5831']
DOI: https://doi.org/10.1007/s00208-021-02254-y