Legendre-Hadamard conditions for two-phase configurations

نویسندگان

  • Yury Grabovsky
  • Lev Truskinovsky
چکیده

We generalize the classical Legendre-Hadamard conditions by using quadratic extensions of the energy around a set of two configurations and obtain new algebraic necessary conditions for nonsmooth strong local minimizers. The implied bounds of stability are easily accessible as we illustrate on a nontrivial example where quasiconvexification is unknown.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A numerical technique for solving a class of 2D variational problems using Legendre spectral method

An effective numerical method based on Legendre polynomials is proposed for the solution of a class of variational problems with suitable boundary conditions. The Ritz spectral method is used for finding the approximate solution of the problem. By utilizing the Ritz method, the given nonlinear variational problem reduces to the problem of solving a system of algebraic equations. The advantage o...

متن کامل

Application of the discrete Fourier transform to the search for generalised Legendre pairs and Hadamard matrices

We introduce Legendre sequences and generalised Legendre pairs (G Lpairs). We show how to construct an Hadamard matrix of order 2£ + 2 from a GL-pair of length f. We review the known constructions for GLpairs and use the discrete Fourier transform (DFT) and power spectral density (PSD) to enable an exhaustive search for GL-pairs for lengths f ::::; 47 and partial searches for other f, 1 Definit...

متن کامل

Closed Analytical Expressions for Some Useful Sums and Integrals Involving Legendre Functions

In Ref. [ 1 ] we have obtained in three different ways the components of the vector magnetic potential (VMP) for the toroidal solenoid. As they satisfy the same equations and the same boundary conditions, they should coincide everywhere (see, e.g., [2]). By comparing these components one can derive simple closed analytical expressions for some integrals and sums involving Legendre functions. Th...

متن کامل

Fractional-order Legendre wavelets and their applications for solving fractional-order differential equations with initial/boundary conditions

In this manuscript a new method is introduced for solving fractional differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use fractional-order Legendre wavelets and operational matrix of fractional-order integration. First the fractional-order Legendre wavelets (FLWs) are presented. Then a family of piecewise functions is proposed, based on whi...

متن کامل

Numerical modeling of three-phase flow through a Venturi meter using the LSSVM algorithm

One of the challenging problems in the Oil & Gas industry is accurate and reliable multiphase flow rate measurement in a three-phase flow. Application of methods with minimized uncertainty is required in the industry. Previous developed correlations for two-phase flow are complex and not capable of three-phase flow. Hence phase behavior identification in different conditions to designing and mo...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016