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Journal of Convex Analysis 18 (2011), No. 4, 1025--1045
Copyright Heldermann Verlag 2011

Comparing Various Methods of Resolving Differential Inclusions

Mikhail A. Sychev
Sobolev Institute for Mathematics, Koptuyg Avenue 4, Novosibirsk 630090, Russia

We compare all existing methods of resolving the homogeneous differential inclusion problem. We emphasize that there is an elementary approach to construct solutions as limit of strongly convergent sequences of approximate solutions. We discuss which role plays an universal functional which measures maximal oscillations produced by admissible for the problem functions at a given one. We suggest a constructive way to generate stable solutions of the inclusions. Finally we prove higher regularity of solutions of the inclusions.

Keywords: Functional analysis, calculus of variations, PDE, differential inclusions, sequences obtained by almost maximal perturbations, stable solutions, higher regularity.

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