Introduction to sublinear analysis

I. V. Orlov

Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 53 (2014), pp. 64-132.

Résumé

Basing on the notion of compact subdifferentials, we develop a subdifferential calculus of the first and the second orders beyond the Taylor expansion and extremum theory. We introduce and investigate a comprehensive class of subsmooth maps such that the constructed theory is applicable to them. We develop a technique to investigate one-dimensional extremal variational problems with subsmooth Lagrangians (including sufficient conditions). A number of examples are considered.

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