Majorisation with Applications to the Calculus of Variations
نویسنده
چکیده
This paper explores some connections between rank one convexity, multiplicative quasiconvexity and Schur convexity. Theorem 5.1 gives simple necessary and sufficient conditions for an isotropic objective function to be rank one convex on the set of matrices with positive determinant. Theorem 6.2 describes a class of non-polyconvex but multiplicative quasiconvex isotropic functions. Relevance of Schur convexity for the description of rank one convex hulls is explained. MSC 2000: 74A20 (primary), 14A42 (secondary)
منابع مشابه
An analytic study on the Euler-Lagrange equation arising in calculus of variations
The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...
متن کاملNON-POLYNOMIAL SPLINE FOR THE NUMERICAL SOLUTION OF PROBLEMS IN CALCULUS OF VARIATIONS
A Class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Convergence anal...
متن کاملBifurcation in a variational problem on a surface with a constraint
We describe a variational problem on a surface under a constraintof geometrical character. Necessary and sufficient conditions for the existence ofbifurcation points are provided. In local coordinates the problem corresponds toa quasilinear elliptic boundary value problem. The problem can be consideredas a physical model for several applications referring to continuum medium andmembranes.
متن کاملNon-Newtonian Fuzzy numbers and related applications
Although there are many excellent ways presenting the principle of the classical calculus, the novel presentations probably leads most naturally to the development of the non-Newtonian calculus. The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Since this self-contained work is intended for a wide audience, inc...
متن کاملA determinant inequality and log-majorisation for operators
Let $lambda_1,dots,lambda_n$ be positive real numbers such that $sum_{k=1}^n lambda_k=1$. In this paper, we prove that for any positive operators $a_1,a_2,ldots, a_n$ in semifinite von Neumann algebra $M$ with faithful normal trace that $t(1)
متن کامل