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Title: The Role of Non-Negative Polynomials For Rank-One Convexity and Quasi Convexity
Authors: Bandeira, Luís
Pedregal, Pablo
Editors: Chipot, Michel
Keywords: Rank-one convexity
quasi convexity
non-negative polynomials
Issue Date: 9-Jan-2017
Publisher: Springer
Citation: Bandeira, L. & Pedregal, P. J Elliptic Parabol Equ (2016) 2: 27.
Abstract: We stress the relationship between the non-negativeness of polynomials and quasi convexity and rank-one convexity. In particular, we translate the celebrated theorem of Hilbert ([3]) about non-negativeness of polynomials and sums of squares, into a test for rank-one convex functions defined on 2 × 2-matrices. Even if the density for an integral functional is a fourth-degree, homogeneous polynomial, quasi convexity cannot be reduced to the non-negativeness of polynomials of a fixed, finite number of variables.
Type: article
Appears in Collections:CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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