A note on the extreme points of the cone of quasiconvex quadratic forms\n with orthotropic symmetry

2018/05/21 by Davit Harutyunyan, Harutyunyan, Davit
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Mathematical functions and polynomials #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1805.08312

openalex publication_date 2018/05/21 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We study the extreme points of the cone of quasiconvex quadratic forms with\nlinear elastic orthotropic symmetry. We prove that if the determinant of the\nacoustic matrix of the associated forth order tensor of the quadratic form is\nan extremal polynomial, then the quadratic form is an extreme point of the cone\nin the same symmetry class. The extremality of polynomials and quadratic forms\nhere is understood in classical convex analysis sense.\n

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