Abstract

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∈KDu\in K.

Author information

Contact details are reproduced from the original publication and may be historical.

Agnieszka Kałamajska

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

kalamajs@mimuw.edu.pl

Keywords

  • Nonconvex variational problems
  • differential inclusions
  • quasiconvexity

Mathematics Subject Classification

49J45, 49J24, 35F30

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Suggested citation

A. Kałamajska. “Lusin Type Theorem with Convex Integration and Quasiconvex Hulls of Sets.” Journal of Convex Analysis 16 (2009), No. 1, 227–237. https://doi.org/10.68381/jca16012

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Published by Heldermann Verlag, 2009. Rights now held by Banach Press.