Régularité de l'enveloppe convexe

Bernd Kirchheim; Jan Kristensen

doi:10.1016/S0764-4442(01)02117-6

Régularité de l'enveloppe convexe

Translated title of the contribution: Differentiability of convex envelopes

Bernd Kirchheim
, Jan Kristensen

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

43 Citations (Scopus)

Abstract

We prove that the convex envelope of a differentiable, or C^1,a-function f is C¹, or C^1,a respectively, provided only that the function satisfies the very mild growth condition that f(x) tends to +8 if |x| does so. © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.

Translated title of the contribution	Differentiability of convex envelopes
Original language	French
Pages (from-to)	725-728
Number of pages	4
Journal	Comptes Rendus de l'Académie des Sciences - Series I - Mathematics
Volume	333
Issue number	8
DOIs	https://doi.org/10.1016/S0764-4442(01)02117-6
Publication status	Published - Oct 2001

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title = "R{\'e}gularit{\'e} de l'enveloppe convexe",

abstract = "We prove that the convex envelope of a differentiable, or C1,a-function f is C1, or C1,a respectively, provided only that the function satisfies the very mild growth condition that f(x) tends to +8 if |x| does so. {\textcopyright} 2001 Acad{\'e}mie des sciences/{\'E}ditions scientifiques et m{\'e}dicales Elsevier SAS.",

author = "Bernd Kirchheim and Jan Kristensen",

year = "2001",

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journal = "Comptes Rendus de l'Acad{\'e}mie des Sciences - Series I - Mathematics",

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AU - Kristensen, Jan

PY - 2001/10

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N2 - We prove that the convex envelope of a differentiable, or C1,a-function f is C1, or C1,a respectively, provided only that the function satisfies the very mild growth condition that f(x) tends to +8 if |x| does so. © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.

AB - We prove that the convex envelope of a differentiable, or C1,a-function f is C1, or C1,a respectively, provided only that the function satisfies the very mild growth condition that f(x) tends to +8 if |x| does so. © 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.

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U2 - 10.1016/S0764-4442(01)02117-6

DO - 10.1016/S0764-4442(01)02117-6

M3 - Article

VL - 333

SP - 725

EP - 728

JO - Comptes Rendus de l'Académie des Sciences - Series I - Mathematics

JF - Comptes Rendus de l'Académie des Sciences - Series I - Mathematics

IS - 8

ER -

Régularité de l'enveloppe convexe

Abstract

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