Relaxation results for functions depending on polynomials changing sign on rank-one matrices

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:349

Article

Boussaid, Omar

关键词: Quasi-convex;    Rank-one convex;    Polyconvex envelopes;    Polynomial of several variables;    Calculus of variations;   

DOI  :  10.1016/j.jmaa.2008.06.047

来源: Elsevier

【 摘 要 】

In this paper, we are interested in computing the different convex envelopes of functions depending on polynomials, especially those having it is main part change sign on rank-one matrices. Our main result applies to functions of the type W(F) = phi(P(F)), W(F) phi(P(F)) + f (det F) or W(F) = phi(P(F)) + g(adj(n) F) defined on the space of matrices, where phi, f : R -> R and g : R(3) -> R are three continuous functions, and P = P(0) + P(1) +... + P(d) is a polynomial such that Pd has the property of changing sign on rank-one matrices. Then the polyconvex, quasi-convex and rank-one convex envelopes of W are equal. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free