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Transactions of the American Mathematical Society

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Optimal regularity of the convex envelope


Authors: Guido De Philippis and Alessio Figalli
Journal: Trans. Amer. Math. Soc. 367 (2015), 4407-4422
MSC (2010): Primary 49J52
DOI: https://doi.org/10.1090/S0002-9947-2014-06306-X
Published electronically: July 21, 2014
MathSciNet review: 3324933
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Abstract: We prove sharp regularity results for the convex envelope of a continuous function inside a convex domain.


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Additional Information

Guido De Philippis
Affiliation: Scuola Normale Superiore, p.za dei Cavalieri 7, I-56126 Pisa, Italy
Email: guido.dephilippis@sns.it

Alessio Figalli
Affiliation: Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Austin, Texas 78712
Email: figalli@math.utexas.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06306-X
Received by editor(s): January 31, 2013
Received by editor(s) in revised form: February 20, 2013, and October 17, 2013
Published electronically: July 21, 2014
Article copyright: © Copyright 2014 American Mathematical Society