An existence theorem and weak Lagrange equations for a variational problem of the theory of phase transitions
type: Item
instance of: scholarly article
title: An existence theorem and weak Lagrange equations for a variational problem of the theory of phase transitions
zbMATH Open document ID: 0866.49003
DOI: 10.1007/BF02106618
published in: Siberian Mathematical Journal
publication date: 1997-07-08T00:00:00Z
review text: The model of phase transitions in continuous media according to which the total energy of a system consists of the sum of energies of deformation of each of the phases and the area of the interface is considered. For that model an existence theorem for a global minimum and weak Lagrange equations for the energy functional are investigated. To overcome the difficulty connected with the rather complicated structure of the area of the interface between the phases, the perimeter of the set occupied by one of the phases is applied. If the set has a sufficiently smooth boundary then its perimeter coincides with the area of the interface. It is also proved that under additional smoothness the weak Lagrange equations transform into the classical Lagrange equations and a system of boundary conditions on the interface.
reviewed by: Wiesław Kotarski
Mathematics Subject Classification ID: 49J10
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
Mathematics Subject Classification ID: 49S05
zbMATH DE Number: 917095
zbMATH Keywords: existence of solutions
zbMATH Keywords: model of phase transitions
zbMATH Keywords: global minimum
zbMATH Keywords: weak Lagrange equations
zbMATH Keywords: energy functional
author: V. G. Osmolovskij
MaRDI profile type: Publication
cites work: Q4002729
description: scientific article; zbMATH DE number 917095