Free and constrained equilibrium states in a variational problem on a surface

Author(s):

Panayotis Vyridis

Abstract:
We study the equilibrium states for an energy functional with a parametric force field on a region of a surface. Consideration of free equilibrium states is based on Lyusternik - Schnirelman''s and Skrypnik''s variational methods. Consideration of equilibrium states under a constraint of geometrical character is based on an analog of Skrypnik''s method, described in cite{vyr3}. In local coordinates, equilibrium points satisfy an elliptic boundary value problem.
Keywords:

Calculus of Variations , Critical points for the Energy Functional , Boundary Value Problem for an Elliptic PDE , Surface , Curvature

Language:
English
Published:
International Journal Of Nonlinear Analysis And Applications, Volume:6 Issue: 3, Summer - Autumn 2015
Pages:
119 to 134
https://www.magiran.com/p1386141