Extension of convex functions from a hyperplane to a half-space

John M. Ball; Christopher L. Horner

doi:10.1007/s00526-024-02719-3

Extension of convex functions from a hyperplane to a half-space

John M. Ball^*, Christopher L. Horner

^*Corresponding author for this work

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

62 Downloads (Pure)

Abstract

It is shown that a possibly infinite-valued proper lower semicontinuous convex function on Rn has an extension to a convex function on the half-space Rⁿ×[0, ∞) which is finite and smooth on the open half-space Rⁿ×(0, ∞). The result is applied to nonlinear elasticity, where it clarifies how the condition of polyconvexity of the free-energy density ψ(Dy) is best expressed when ψ(A)→∞ as detA→0+.

Original language	English
Article number	107
Journal	Calculus of Variations and Partial Differential Equations
Volume	63
Issue number	4
Early online date	17 Apr 2024
DOIs	https://doi.org/10.1007/s00526-024-02719-3
Publication status	Published - May 2024

Keywords

74B20
49J45
26B25

Access to Document

10.1007/s00526-024-02719-3Licence: CC BY

Download pdf
© The Author(s) 2024.
Final published version, 267 KBLicence: CC BY

Cite this

@article{b6541605d3194a578e20acf6e4dc2bbe,

title = "Extension of convex functions from a hyperplane to a half-space",

abstract = "It is shown that a possibly infinite-valued proper lower semicontinuous convex function on Rn has an extension to a convex function on the half-space Rn×[0, ∞) which is finite and smooth on the open half-space Rn×(0, ∞). The result is applied to nonlinear elasticity, where it clarifies how the condition of polyconvexity of the free-energy density ψ(Dy) is best expressed when ψ(A)→∞ as detA→0+.",

keywords = "74B20, 49J45, 26B25",

author = "Ball, \{John M.\} and Horner, \{Christopher L.\}",

year = "2024",

month = may,

doi = "10.1007/s00526-024-02719-3",

language = "English",

volume = "63",

journal = "Calculus of Variations and Partial Differential Equations",

issn = "0944-2669",

publisher = "Springer New York",

number = "4",

}

TY - JOUR

T1 - Extension of convex functions from a hyperplane to a half-space

AU - Ball, John M.

AU - Horner, Christopher L.

PY - 2024/5

Y1 - 2024/5

N2 - It is shown that a possibly infinite-valued proper lower semicontinuous convex function on Rn has an extension to a convex function on the half-space Rn×[0, ∞) which is finite and smooth on the open half-space Rn×(0, ∞). The result is applied to nonlinear elasticity, where it clarifies how the condition of polyconvexity of the free-energy density ψ(Dy) is best expressed when ψ(A)→∞ as detA→0+.

AB - It is shown that a possibly infinite-valued proper lower semicontinuous convex function on Rn has an extension to a convex function on the half-space Rn×[0, ∞) which is finite and smooth on the open half-space Rn×(0, ∞). The result is applied to nonlinear elasticity, where it clarifies how the condition of polyconvexity of the free-energy density ψ(Dy) is best expressed when ψ(A)→∞ as detA→0+.

KW - 74B20

KW - 49J45

KW - 26B25

UR - https://www.scopus.com/pages/publications/85190555233

U2 - 10.1007/s00526-024-02719-3

DO - 10.1007/s00526-024-02719-3

M3 - Article

SN - 0944-2669

VL - 63

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

M1 - 107

ER -

Extension of convex functions from a hyperplane to a half-space

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this