Title of article :
Free and constrained equilibrium states in a variational problem on a surface
Author/Authors :
Vyridis, Panayotis Department of Physics and Mathematics - National Polytechnical Institute (I.P.N.) - Campus Zacatecas (U.P.I.I.Z) - Zacatecas, Mexico
Abstract :
We study the equilibrium states for an energy functional with a parametric force eld 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 [P. Vyridis, Bifurcation in a
Variational Problem on a Surface with a Constraint, Int. J. Nonlinear Anal. Appl. 2 (1) (2011),
1-10]. 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
Journal title :
Astroparticle Physics
