On various semiconvex hulls in the calculus of variations

Kewei Zhang

On various semiconvex hulls in the calculus of variations

Kewei Zhang

School of Mathematical & Computer Sciences

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

24 Citations (Scopus)

Abstract

We show that for any compact set K ? M^N×n, L_C(K) = C(K) if and only if Q(K) = C(K), L_C(K), Q(K) and C(K) being the closed lamination convex hull, quasiconvex hull and convex hull of K respectively. When K ? M^2×2, we show that L_C(K) = C(K) if and only if P(K) = C(K), where P(K) is the polyconvex hull of K. We give some estimates of these relations by using quasiconvexifications of distance functions.

Original language	English
Pages (from-to)	143-160
Number of pages	18
Journal	Calculus of Variations and Partial Differential Equations
Volume	6
Issue number	2
Publication status	Published - 1998

Cite this

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title = "On various semiconvex hulls in the calculus of variations",

abstract = "We show that for any compact set K ? MN×n, LC(K) = C(K) if and only if Q(K) = C(K), LC(K), Q(K) and C(K) being the closed lamination convex hull, quasiconvex hull and convex hull of K respectively. When K ? M2×2, we show that LC(K) = C(K) if and only if P(K) = C(K), where P(K) is the polyconvex hull of K. We give some estimates of these relations by using quasiconvexifications of distance functions.",

author = "Kewei Zhang",

year = "1998",

language = "English",

volume = "6",

pages = "143--160",

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

issn = "1432-0835",

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number = "2",

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T1 - On various semiconvex hulls in the calculus of variations

AU - Zhang, Kewei

PY - 1998

Y1 - 1998

N2 - We show that for any compact set K ? MN×n, LC(K) = C(K) if and only if Q(K) = C(K), LC(K), Q(K) and C(K) being the closed lamination convex hull, quasiconvex hull and convex hull of K respectively. When K ? M2×2, we show that LC(K) = C(K) if and only if P(K) = C(K), where P(K) is the polyconvex hull of K. We give some estimates of these relations by using quasiconvexifications of distance functions.

AB - We show that for any compact set K ? MN×n, LC(K) = C(K) if and only if Q(K) = C(K), LC(K), Q(K) and C(K) being the closed lamination convex hull, quasiconvex hull and convex hull of K respectively. When K ? M2×2, we show that LC(K) = C(K) if and only if P(K) = C(K), where P(K) is the polyconvex hull of K. We give some estimates of these relations by using quasiconvexifications of distance functions.

UR - https://www.scopus.com/pages/publications/0000881815

M3 - Article

SN - 1432-0835

VL - 6

SP - 143

EP - 160

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 2

ER -

On various semiconvex hulls in the calculus of variations

Abstract

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