scholarly journals Local completeness of locally pseudoconvex spaces and Borwein–Preiss variational principle

2007 ◽  
Vol 183 (2) ◽  
pp. 99-115 ◽  
Author(s):  
J. H. Qiu ◽  
S. Rolewicz
Keyword(s):  
Variational Principle ◽  
Local Completeness

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

On a strong minimum condition of a fractal variational principle

2021 ◽  
pp. 107199
Author(s):  
Ji-Huan He ◽  
Na Qie ◽  
Chun-hui He ◽  
Tareq Saeed
Keyword(s):  
Variational Principle ◽  
Minimum Condition

ALMOST ADDITIVE THERMODYNAMIC FORMALISM: SOME RECENT DEVELOPMENTS

2010 ◽  
Vol 22 (10) ◽  
pp. 1147-1179 ◽  
Author(s):  
LUIS BARREIRA
Keyword(s):  
Variational Principle ◽  
Existence And Uniqueness ◽  
Gibbs Measures ◽  
Thermodynamic Formalism ◽  
Topological Pressure ◽  
Present Stage ◽  
The Past ◽  
Recent Developments ◽  
General Sequences ◽  
Uniqueness Of Equilibrium

This is a survey on recent developments concerning a thermodynamic formalism for almost additive sequences of functions. While the nonadditive thermodynamic formalism applies to much more general sequences, at the present stage of the theory there are no general results concerning, for example, a variational principle for the topological pressure or the existence of equilibrium or Gibbs measures (at least without further restrictive assumptions). On the other hand, in the case of almost additive sequences, it is possible to establish a variational principle and to discuss the existence and uniqueness of equilibrium and Gibbs measures, among several other results. After presenting in a self-contained manner the foundations of the theory, the survey includes the description of three applications of the almost additive thermodynamic formalism: a multifractal analysis of Lyapunov exponents for a class of nonconformal repellers; a conditional variational principle for limits of almost additive sequences; and the study of dimension spectra that consider simultaneously limits into the future and into the past.

scholarly journals Variational Methods for Glacier Mechanics Problems

1981 ◽  
Vol 27 (95) ◽  
pp. 19-24 ◽  
Author(s):  
Robert G. Oakberg
Keyword(s):  
Finite Element ◽  
Melting Point ◽  
Variational Principle ◽  
Finite Element Model ◽  
Related Problem ◽  
Cylindrical Channel ◽  
Direct Methods ◽  
Approximate Solutions ◽  
Element Model ◽  
Coordinate Functions

AbstractThe object of the research is to determine whether direct methods from the calculus of variations can provide convenient approximate solutions of complex problems in glacier mechanics. The Ritz technique is used to minimize an appropriate functional. Coordinate functions obtained from a finite-element model are combined with a coordinate function that is the solution of a related problem. The finite-element coordinate functions make localized adjustments to the related solution. Solutions of two sample problems are presented. An analysis of the closure of an intergranular vein in ice at the melting point is based upon a variational principle for velocities. An analysis of the flow of ice in a cylindrical channel is based upon a variational principle for stresses.

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