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This article is cited in 15 scientific papers (total in 16 papers)
On a property of the subdifferential
A. I. Subbotin Institute of Mathematics and Mechanics, Ural Branch of the AS of USSR
Abstract:
Semicontinuous real functions are considered. The following property is established for the Dini directional semiderivative and the Dini semidifferential (the subdifferential). If at some point the semiderivative is positive in a convex cone of directions, then arbitrarily close to the point under consideration there exists a point at which the function is subdifferentiable and has a subgradient belonging to the positively dual cone. This result is used in the theory of the Hamilton–Jacobi equations to prove the equivalence of various types of definitions of generalized solutions.
Received: 08.02.1990
Citation:
A. I. Subbotin, “On a property of the subdifferential”, Math. USSR-Sb., 74:1 (1993), 63–78
Linking options:
https://www.mathnet.ru/eng/sm1370https://doi.org/10.1070/SM1993v074n01ABEH003335 https://www.mathnet.ru/eng/sm/v182/i9/p1315
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