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Journal of Convex Analysis 16 (2009), No. 1, 227--237
Copyright Heldermann Verlag 2009

Lusin Type Theorem with Convex Integration and Quasiconvex Hulls of Sets

Agnieszka Kalamajska
Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland

We obtain Lusin type theorem showing that after extracting an open set of an arbitrary small measure one can apply the variant of convex integration theory dealing with quasiconvex hulls of sets. The result is applied to the existence theory of approximate solutions of the PDI: Du belongs to K.

Keywords: Nonconvex variational problems, differential inclusions, quasiconvexity.

MSC: 49J45, 49J24, 35F30

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