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 - http://www.scopus.com/inward/record.url?scp=85190555233&partnerID=8YFLogxK
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 -